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EASY LESSONS 


IK 

MENTAL ARITHMETIC, 

UPOK THE 

INDUCTIVE METHOD; 

ADAPTED TO THE 

BEST MODE OF INSTRUCTION IN PRIMARY SCHOOLS. 


BY 

JAMES S. EATON, M.A. 

INSTRUCTOR IN PHILLIPS ACADEMY, ANDOVER, AND AUTHOR OF 
A TREATISE ON ^RITTEN ARITHMETIC* 


9 

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BOSTON: 

THOMPSON, BROWN, & CO. 

1 8 76 . 











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Entered according to Act of Congress, in the year 1860, by 
JAMES S. EATON, 

In the Clerk’s Office of the District Court of the District of Massachusetts. 


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FRANKLIN PRESS: 
RAND, AVERY, & CO. 
















1 


PRE FA C E . 


The author has prepared this little book both in compliance 
with the solicitation of Teachers and others interested in his 
larger work, and with the desire to present the first principles of 
the science in a form to interest the youngest members of our 
Primary Schools. 

Definitions and extended explanations, being generally unin¬ 
telligible, and therefore uninteresting and unprofitable, to young 
children, have been carefully avoided, and the simplest opera¬ 
tions in numbers have been presented in the most familiar man¬ 
ner, separately or in combination, as seemed most likely to 
interest and benefit the pupil. 

No effort has been spared to make the book simple in lan¬ 
guage, varied in expression, progressive in style, and attractive 
in illustration; and thus, it is hoped, the little learner will form 
accurate habits, and unconsciously become familiar with such 
simple calculations as shall prepare him to enter with pleasure 
upon the more vigorous thinking required in the Author’s In¬ 
tellectual. Arithmetic. 

In the preparation of these Lessons, the author has received 
valuable aid from Teachers, eminent in their profession, and 
familiar with the best modes of instruction in Primary Schools 

Phillips Academv, Andover, 

June 9, 1860 










SUGGESTIONS TO TEACHERS 


A knowledge of numerical calculation is not the only, 
perhaps not the most important, object to be attained in the 
study of a work like this. The child is to be interested; his 
attention secured; the power of abstraction created; his mind 
disciplined, in preparation for other and higher pursuits. 

The benefits derived in any study, preeminently in an ele¬ 
mentary study, depend, in great measure, upon the methods 
employed in teaching it. These pages are designed only as 
specimen lessons. A large share of the instruction in Primary 
Arithmetic should be oral; and certainly no Teacher in this de¬ 
partment would ever think of following, literally, the lessons of 
any book, however perfect the book may be. 

The skillful Teacher will vary the manner of presenting an 
idea to meet the ever-varying wants of the day, the lesson and 
the pupil. The golden mean between too little and too much 
explanation should be selected. Most teachers, especially the 
inexperienced, pass over first principles too rapidly. The 
groundwork must be carefully and thoroughly prepared, or 
real progress is impossible. 

Let the pupil repeat, and repeat again, and vary the expres¬ 
sion, until he is perfect master of the thought. Incorporate in 
his very being the idea that 3 and 4 is the same as 4 and 3; 
that 5 times 6 is the same as 6 times 5; that 8 and 8 is identical 
with twice 8, etc., etc.; and his subsequent progress will be sure, 
and rapid, and pleasant. 





PRIMARY ARITHMETIC. 


LESSON I. 

John has one apple in his right hand, and 
one apple in his left hand; how 
many apples has he in both hands ? 

One apple and one apple are 
how many apples ? 

How many hands has John ? 
One hand and one hand are 
how many hands ? 

Has John two feet? Count 
them. One, two. 

How many eyes has John ? 

One eye and one eye are how 
many eyes? 

John had two apples in his left hand, but he 
has taken one of them in his right hand; how 
many has he in his left hand now? 

One apple taken from two apples leaves how 
many apples ? 

Point to John’s right hand. Point to his left 
hand. 

One and one are how many ? One from two 
leaves how many ? 



1* 




6 PRIMARY ARITHMETIC. 


LESSON II. 

Willie had two apples, and Mary has given 
him one more ; how many 
apples has Willie now? 

How many apples has 
Willie in his right hand ? 

How many has he in his 
left hand ? How many in 
both hands ? 

Two apples and one ap-. 
pie are how many apples ? 

One apple and two ap¬ 
ples are how many apples ? 

How many more apples 
has Willie in his right 
hand than in his left ? 

How many less in his left hand than in his 
right ? 

Two and one more are how many ? 

One and two more are how many ? 

Which is the greater number, two and one 
more, or one and two more ? 

Answer. — Neither ; they are the same. 

Two are how many more than one ? 

One is how many less than two ? 

Both of Mary’s eyes, and one of Willie’s, are 
in sight; how many eyes can you see in the 
picture ? 

Which of Willie’s eyes is in sight ? 

Willie has two feet, and Mary has two feet; 
how many feet have Willie and Mary together ? 
How many apples are there in Mary’s basket ? 








PRIMARY ARITHMETIC. 


7 


LESSON III. 

How many can you count ? 

You may count the blocks in each of these 
rows. 



Which is the left side of this page ? Which 
the right? 

You may count the blocks in each of these 
rows, beginning at the left side of the page, and 
counting from the bottom to the top. 

One block and two blocks are how many 
blocks ? 







PRIMARY ARITHMETIC. 


8 


LESSON IV. 



Oue ox and one ox are how many oxen ? 
One and one are how many ? 



Two horses and one horse are how many 
horses ? 

Two and one are how many ? One and two ? 



Three sheep and one sheep are how many 
sheep ? 

Three and one are how many? One and three? 



Four goats and one goat are how many goats ? 
Four and one are how many? One and four? 



Five dogs and one dog are how many dogs ? 
Five and one are how many? One and five ? 









PRIMARY ARITHMETIC. 


9 



Six chickens are running one way, and one 
is running another way; liow many chickens 
are there in the picture : 

Six and one are how many ? One and six ? 



A flock of birds are on the ground ; seven of 
them have nothing to eat, but one has a nice 
ripe cherry; how many birds are there in the 
flock ? 

Seven and one are how many ? One and 
seven ? 



Eight birds are standing on a limb of a tree, 
and one is on the ground; how many birds are 
there in the flock ? 

Eight and one are how many ? One and 
eight ? 



Nine chickens are running towards the left, 
and one towards the right; how many chickens 
are there in the brood ? 

Nine and one are how many ? One and nine ? 





10 PRIMARY ARITHMETIC. 



A flock of snow-birds have lighted, ten of 
them upon the branch of a tree, and one upon 
the ground; how many birds are there in the 
flock ? 

Ten and one are how many ? One and ten ? 


LESSON V. 



James has two sleds, and Willie has one sled; 
how many sleds have they both ? 

How many are two and one ? One and two ? 



Two wagons and two wagons are how many 
wagons ? 

How many are two and two ? 



Mr. Fox bought two wheelbarrows, and Mr. 
Hale bought three; how many did they both 
buy ? 

IIow many are two and three ? Three and 
two ? 










PRIMARY ARITHMETIC. 


11 



Charles made two kites, and Edward made 
four; how many kites did Charles and Edward 
both make ? 

How many are two and four ? Four and two ? 

oo ooooo 

Mary has two hoops, and Lizzie has five ; how 
many hoops have Mary and Lizzie together ? 
How many are two and five ? Five and two ? 



Two balls and six balls are how many balls? 
Two and six are how many ? Six and two ? 



George owns two bows, and Thomas owns 
seven ; how many bows do George and Thomas 
both own ? 

Two and seven are how many ? Seven and 
two ? 

V V V V V 

/\ /\ /\ /\ /\ 

Two arrows and eight arrows are how many 
arrows ? 

Two and eight are how many ? Eight and two ? 





12 PRIMARY ARITHMETIC. 



Here are two tops spinning in one place, and 
nine in another; liow many tops are spinning 
in the two places ? 

Two tops and nine tops are how many tops ? 
Two and nine are how many ? Nine and two ? 



Two knife-blades and ten knife-blades are 
how many knife-blades ? 

Two and ten are how many ? Ten and two ? 


LESSON VI. 



One apple and three apples are how many 
apples ? 

How many are one and three ? Three and one ? 



A kind lady gave two pears to Georgie, and 
three to Willie; how many pears did she give 
to both of them ? 

How many are two and three? Three and two? 






PRIMARY ARITHMETIC. 13 



How many oranges are three oranges and 
three oranges? 

How many are three and three ? 



Four peaches grew on one little tree, and 
three grew on another; how many grew on 
both ? 

Four and three are how many ? Three and 
four ? 



Five lemons were used in making one pailful 
of lemonade, and three in making another ; how 
many were used in making the two pailfuls ? 



Six plums and three plums are how many 
plums ? 

Six and three are how many ? Three and six ? 



Seven and three blackberries are how many 
blackberries ? 

Seven and three are how many ? Three and 
seven ? 




14 PRIMARY ARITHMETIC. 



Eight acorns are in one row, and three in 
another row; how many acorns are in both 
rows ? 

Eight and three are how many ? Three and 
eight ? 



Ad die found nine large red strawberries, and 
Ella found three; how many did both of them 
find ? 

Nine and three are how many ? Three and 
nine ? 



Ten stems of currants grew on one bush, and 
three stems grew on another bush; how many 
stems grew on both bushes ? 

Ten and three are how many? Three and ten ? 
How many are six and three and four ? 

How many are three and six and four ? 




PRIMARY ARITHMETIC. 


15 


LESSON VII. 



One pig and four pigs are how many pigs ? 
One and four are liow many ? Four and one ? 



Two cats and four cats are how many cats ? 
Two and four are how many ? Four and two ? 



Alfred has three tame rabbits, and Asa lias 
four; how many rabbits have Alfred and Asa ? 

Three and four are how many ? Four and 
three ? 



Four squirrels are eating nuts in one row, 
and four in another row; how many squirrels 
are eating nuts ? 

How many are four and four ? 



Here are five rats for pussy, and here are four 
more ; how many rats are there for pussy ? 

How many are five and four ? Four and five ? 





16 PRIMARY ARITHMETIC. 



Six apples and four apples are how many 
apples ? 

How many are six and four ? Four and six ? 


Seven, balls and four balls are how many 
balls ? 

How many are seven and four ? Four and 
seven ? 

Eiglit balls and four balls are how many 
balls ? 

Eight and four are how many ? Four and 
eight ? 

■ 0 0 - 0 - 0 -0 0 --- 0 . 0 ^ - 0 . 

Nine and four are how many ? Four and nine ? 


- 0 - 0 - 0 - 00 - 0 - 0 - Q-0-0— — GhO-Q~Q- 

How many are ten and four ? Four and ten ? 
How many are three and two ? Two and three ? 
How many are two and six ? Six and two ? 
How many are two and eight ? Eight and two ? 
How many are two and nine ? Nine and two ? 
How many are three and three ? 

How many are two and seven ? Seven and two ? 
How many are three and three and five ? 







PRIMARY ARITHMETIC. 


17 


LESSON VIII. 




One acorn and five acc/ns are how many 
acorns ? 




Two tops and five tops are how many tops? 


Three balls and five balls are how many balls ? 
Four and five are how many ? Five and four ? 



Six and five are how many ? Five and six ? 

IIow many are eight and five ? Five and 
eight ? 

—■—0-0-Q-0-0- 

Ten and five are how many ? Five and ten ? 
How many arc five and five ? 

How many are nine and five ? Five and nine ? 


2* 














18 PRIMARY ARITHMETIC. 


LESSON IX. 

Here is a happy group of children. How 
earnestly they play! They are good children, 
and love to study, as well as play. The teacher 
is ringing the bell for them ; but we will count 
them before they go in. One, two, three, four, 
five boys ; one, two, three, four, live girls. 

Five boys and live girls are how many chil¬ 
dren ? Five and live are how many ? 

One boy and one girl are driving hoop ; how 
many are driving hoop ? 



















PRIMARY ARITHMETIC. 19 


Two boys and one girl are playing catch; 
how many are playing catch ? Two and one 
are how many? One and two? 

Three girls and two boys are jumping rope ; 
how many are jumping rope? Three and two 
are how many ? Two and three ? 

Two children are rolling hoop, three are 
playing catch, and five are jumping rope ; how 
many are two and three and live ? Three and 
two and five ? Five and two and three ? 

There are three posts on one side of the gate, 
and four on the other side ; how many posts are 
there in the fence ? Three and four are how 
many ? Four and three ? 

Four trees stand on one side of the school- 
house, and four on the other; how many trees 
are there on both sides ? How many are four 
and four ? 

There are four windows on the end of the 
house, and five on the front; how many win¬ 
dows do you see in the house ? How many are 
five and four ? Four and five ? 

LESSON X. 

Two geese were near a pond, and one of them 
ran into the "water ; how many 
were left on the land? One 
from two leaves how many ? 

Three turkeys were standing 
together, but one has lain down ; 
how many remain standing ? 

Three less one are how many ? Three less two ? 







PRIMARY ARITHMETIC. 



Charlie had four hens, but gave one to George; 
• how many had he left ? 

One from four leaves how many ? 

One and three are how many ? Three and 
one ? 

Three taken from four leaves how many ? 



Here are five ducks ; one has its head down ; 
how many have their heads up ? 

One from five leaves how many ? 

How many remain if four are taken from 
five ? 

Four and one are how many ? One and four ? 



Daniel has six doves; one of them is dark 
colored, and the rest are white; how many are 
white ? 

One from six leaves how many ? 

How many are one and five ? Five and one ? 



Here are seven little chickens ; one of them 
is running towards the right, and the rest are 











PRIMARY ARITHMETIC. 21 


running towards the left; how many are going 
towards the left ? 

One from seven leaves how many ? 

Seven less six are how many ? 

Six and one are how many V Three and four ? 



One of these robins has a ripe cherry; how 
many have no cherry ? 

How many are one and seven ? Seven and 
one ? 

Eight less one are how many ? Eight less 
seven ? 



Count these sparrows. One is on the ground; 
how many are on the branch ? 

One taken from nine leaves how many ? 

Nine less eight are how many ? 

How many are e T ‘ght and one ? One and 
eight ? 



Here are ten humming-birds. One of them 
is getting honey from a flower; how many 
others do you see in the picture ? 

Ten less one are how many ? Ten less nine ? 
How many are nine and one ? One and nine ? 
How many are six and four ? Four and six ? 









99 


PRIMARY ARITHMETIC. 


LESSON XI. 

Jane has three roses; two of them are buds; 
how many are in full bloom ? 

Two from three leaves how 
many ? One from three ? 

Two and one are how many ? One and two ? 
Three are how many more than two ? 

Three are how many more than one ? 

Sarah gathered four pinks, but broke the 
stems of two of them; how ^ 
many remain unbroken ? 

Two from four leaves how ^ 
Four are how many more than two ? 



many 


Nancy found five tulips; two of them had 
leaves on the stems ; how many had no leaves ? 
Five less two are how many ? 

Five are how many more than three ? 

Here are six field lilies; two of them are 
drooping; how many 
are upright ? 

Two are how many 
less than six ? Six are how many more than 
four ? 

Ellen found seven violets, two of them in the 
^ meadow, and the rest on the 
jpJKj hill; how many did she find 
on the hill ? 

Two from seven leaves how many ? 

Five and two are how many ? Two and five ? 








PRIMARY ARITHMETIC. 23 



Eight clover blossoms are in a flower-bed ; 
two are on one side of the bed; how many 
are on the other side ? Eight less two are 
how many ? Eight less six ? 



Georgie found nine snow-drops, and gave two 
of them to his sister; how many had he re¬ 
maining ? 

Two from nine leaves how many ? 

How many are seven and two ? Two and 
seven ? 



Martha has ten daisies; two of them are white, 
and the rest are pink ; how many are pink ? 
Two from ten leaves how many ? Seven from 
ten? 


LESSON XII. 



Four butterflies were on the ground, but 
three of them are flying away; how many re¬ 
main on the ground ? 

Three from four leaves how many ? 







24 PRIMARY ARITHMETIC. 



Here are six honey-bees; three of them have 
their wings spread ; how many have them closed ? 
Three from six leaves how many ? 



Eight spiders were upon the wall, but three 
j have fallen upon the floor; how many remain 
upon the wall ? 

Three taken from eight leaves how many ? 
Eight are how many more than five ? 



Ten flies were on the window, but three of 
them are caught in a spider’s web; how many 
are still free ? 

Three from ten leaves how many? How 
many are seven and three ? 


LESSON XIII. 



Five stalks of wheat were standing in a field, 
but the wind has broken four of the heads 
down; how many heads still stand upright ? 
Four from five leaves how many ? 

Five are how many more than one ? 











PRIMARY ARITHMETIC. 


25 



Here are seven heads of barley; four of 
them have leaves upon the stalks; how many 
are without leaves ? 

Four from seven leaves how many ? 

How many are seven less three ? 



Emily has nine flowers; four of them are 
pinks, and the rest are tulips; how many are 
tulips ? 

Four from nine leaves how many ? 

Nine are how many more than four ? 



Charlie has eleven chickens; four of them 
are in one brood and the rest are in another ; 
how many are in the other ? 



Four from eleven leaves how many ? 

How many are seven and four ? Four and 
seven ? 

Where are Charlie’s two broods of chickens ? 
Point at them. 

Seven are how many more than four ? 

Four are how many less than seven ? 


3 








PRIMARY ARITHMETIC. 


26 


LESSON XIV. 



A cabinet-maker made six tables; five of 
them were without drawers; liow many had 
drawers ? 


Five from six leaves how many ? 



There are eight chairs in one room; five of 
them have cane seats; how many have wooden 
seats ? 

Five from eight leaves how many ? 

Three and five are how many ? 



Here are nine stools; five of them have 
four legs apiece; how many have only three 
legs apiece ? 

Five taken from nine leaves how many ? 

How many are five and four ? Four and five ? 



In two birds’ nests there are ten eggs; if five 



















PRIMARY ARITHMETIC. 27 

of them are in one nest, how many are in the 
other ? 

Five from ten leaves how many ? 

Five and five are how many ? 

LESSON XV. 

Now, children, as you have learned to count, 
and to add and subtract small numbers, I will 
give you some marks or figures which stand for 
numbers; each figure means the same as the 
word which stands under it: 

1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 . 

One, Two, Three, Four, Five, Six, Seven, Eight, Nine 

Besides these nine figures there is one more, 
which stands for nothing; this is it: 0. It looks 
like the letter 0. We call it zero . It is some¬ 
times called a cipher , and sometimes naught , or 
nothing. 

These ten marks are called Arabic figures, 
because they were used by the Arabs a great 
many hundred years ago. 

When we write the figures, we make them in 
this form: 

O, /, 2, 3, 4, s, 6, 7, e, ffi. 

Naught, One, Two, Three, Four, Five, Six, Seven, Eight, Nine. 

Now you may take your slates and pencils 
and make the figure that stands for one. Make 
the figure that stands for six. We call it the 
figure six. Make the figure four. Make all of 
the figures, and tell what each stands for. 










28 


PRIMARY ARITHMETIC. 


LESSON XVI. 

To aid us in writing larger numbers, we will 
make a little frame of wood and wires, and put 
some balls on the wires. 



Here is a picture of the frame with the balls 
on the wires. We call it the Numeral Frame. 
How many wires are there ? IIow many balls 
on the top wire ? How many on the second 
wire ? On the third ? Fourth ? Fifth ? 

Are there ten balls on each wire ? 

Is there any Arabic figure that stands for 
ten ? No. How, then, shall we write ten ? 

It is written in this way : 10. First we write 
the figure 1, and then put the zero on the right 
of the 1. The 0 is put on the right of the 1 to 
show that the 1 is to stand for once ten balls , and 
not for one single ball. 

























PRIMARY ARITHMETIC. 29 

Now you may make the figures that stand for 
ten. 

We will. Here they are : 10. 

That is right. What figures stand for ten ? 

The figure 1 with a 0 on the right of the 1. 

Very Avell. What does the 1 mean when it 
has a 0 on the right of it ? It means one ten , 
or once ten . 

LESSON XVII. 

How many balls are there on the upper wire ? 
Ten. 

How many on the second wire ? Ten. 

How many on both together ? Twenty. 

How many tens make twenty? Two tens 
make twenty. Here arc the figures that stand 
for twenty: 20. They are the figure 2 with the 
0 on the right of the 2. The zero at the right 
of the 2 shows that the 2 stands for two tens , or 
twice ten balls, and not for two balls. 

Will you make the figures for twenty ? Yes: 
20. What are they ? The figure 2 with 0 at 
the right of it. What does the 2 mean when 
it lias 0 at the right of it ? It means two tens, 
or twenty. How many are twice ten ? Twice 
ten are twenty. 

How many balls are there on the three upper 
wires ? Count them. There are thirty. How 
many tens make thirty ? Three times ten are 
thirty- Can you write the figures for thirty? 
Wo can : 30. What are they ? A3 with 0 at 
the right of it. 









80 PRIMARY ARITHMETIC. 


LESSON XVIII. 



Here are ten balls upon the top wire, and there 
is one ball by itself on the second wire. How 
many are ten balls and one ball? Ten balls 
and one ball are eleven balls. These figures 
stand for ten and one, or eleven : 11. The first 
or left figure 1 stands for once ten balls, and the 
1, at the right hand, stands for the one ball. 

Yon may write the figures for eleven: 11. 
What are they ? They are the figure 1 and the 
figure 1 at the right of the first 1. What does 
the first 1 stand for? What does the second 
one stand for ? How many are 10 and 1 ? 

There are ten balls on the top wire, and two 
balls stand by themselves on the third wire. 
How many are ten and two ? Ten and two are 
twelve. These figures stand for ten and two, 














r 


PRIMARY ARITHMETIC. 


31 


or twelve : 12. The figure 1 stands for the ten, 
and the figure 2, at the right of the 1, stands 
for the two. You may write the figures for 
twelve. Can you write thirteen in figures ? 
Yes: 13. Write fourteen: 14; fifteen: 15; six* 
teen: 16 ; seventeen : 17 ; eighteen: 18 ; nine 
teen: 19. Very well. All right. 

LESSON XIX. 

flow many balls are there on the top wire of 
the Numeral Frame ? Ten. 

How many on the second wire ? Ten. 

How many on both wires ? Twenty. 

Now, if we put one more ball with these 
. twenty, how many balls shall we have ? If 
we put one ball with twenty balls we shall 
have twenty-one balls. These figures stand for 
twenty-one : 21. What figures are they ? They 
are a 2 with a 1 on the right of it. The two 
stands for twenty, or two times ten balls, and the 
1, at the right of the 2, stands for the one ball. 

How do the figures for twenty-one differ from 
those for twelve ? They are the same figures, 
but they are placed differently. How are they 
placed ? For twenty-one, the 2 stands at the 
left of the 1; but for twelve, the 1 stands at the 
left of the 2. When two figures stand for a 
number, the left-hand figure is for the tens and 
the right-hand figure for the ones - 

Now you may write the figures for twenty- 
one : 21. Now write them for twelve : 12. That 
! is right. 

( ___ 










PRIMARY ARITHMETIC. 


32 


i 

1 


If two balls are put with twenty balls, liow 
many balls shall we have ? Twenty balls and 
two balls are twenty-two balls. These figures 
stand for twenty-two: 22. The left-hand 2 
stands for the twenty, or the twice ten balls, 
and the right-hand 2 for the two balls. 

How many are twenty and three ? Twenty 
and three are twenty-three. 

Can you make the figures for twenty-three ? 
Yes: 23. Right. 

Now you may make the figures for twenty- 
four : 24 ; for twenty-five: 25 ; for twenty-six: 
26. What number do these figures stand for: 
27 ? They stand for twenty-seven. These : 28 ? 
For twenty-eight. These: 29 ? For twenty-nine. 


LESSON XX. 

Now I think you can make the figures for 
any number that is less than one hundred. 

You may make the figures for any ten num¬ 
bers you please, and tell me what they stand 
for. We will. 


36 stands for 
63 

47 “ 

49 

94 “ 

77 « 

75 

57 “ 

99 “ 

31 


Thirty-six. 

Sixty-three. 

Forty-seven. 

Forty-nine. 

Ninety-four. 

Seventy-seven. 

Seventy-five. 

Fifty-seven. 

Ninety-nine. 

Thirty-one. 









PRIMARY ARITHMETIC. 33 

Now you may write the words for any ten 
numbers, and then make the figures which mean 
the same. Well. 


Seven 

is the 

same 

as 7 

Seventeen 

a 

u 

17 

Twenty-seven 

u 

u 

27 

Thirty-seven 

a 

a 

37 

Seventy-three 

u 

a 

73 

Thirty-five 

u 

u 

35 

Fifty-three 

a 

u 

53 

Forty-eight 

a 

u 

48 

Nine 

a 

u 

9 

Ninety 

a 

a 

90 

5 the 9 stand for the 

same 

in these last 


two numbers ? It does not. In the last num¬ 
ber it stands for 9 tens, and in the other it stands 
for ^ ones. How do you know it stands for 9 
tens in the last number ? Because there is a 
figure at the right of it, and this shows that it 
is 9 tens. 

How many Arabic figures are there ? Are 
there any other marks that stand for numbers ? 
Yes ; there are seven letters which stand for 
numbers. Here they are : 

I, V, X, L, C, D, M. 

One, Five, Ten, Fifty, One hundred, Five hundred, One thousand. 

These are called Roman figures. The Arabic, 
figures are much better than the Roman, be¬ 
cause they arc easier to use. You will notice 
the manner of using the Roman figures at the 
beginning of these lessons, and perhaps your 
teacher will tell you more about them. 


i. 











34 PRIMARY ARITHMETIC. 


LESSON XXI. 

TnESE little children are having a nice time. 
Carrie has invited five of her playmates to her 
birthday party, and they are playing “take tea” 
with her at the table, while her little brothers 
and sister are amusing themselves on the floor. 
Her mother sits in the great arm-chair, very 
happy to see her children and little friends so 
happy. 

Carrie is pouring tea. How many girls do 
you see at her left hand ? How many at her 






























PRIMARY ARITHMETIC. 35 

right ? How many more on one side than on 
the other ? Two from three leaves how many ? 
Three are how many more than two ? 

Ella is giving the dolls a ride. She put five 
dolls in the wagon, but one of them has fallen 
out; how many remain in ? One from five 
leaves how many ? 

There are three books on the lower shelf of 
the book-case, and two on the next shelf; how 
many books are there on both shelves ? How 
many more on one shelf than on the other ? 

Count the hats hanging upon the hooks. 

How many less in the upper row than in the 
lower ? 

Three from four leaves how many ? 

Three and four are how many ? Four and 
three ? 

Little Arthur is playing with the blocks on 
the floor. Can you count the blocks ? How 
many are there ? How many more on one side 
of him than on the other ? 

How many are five and four ? Five less four ? 

One ox has 4 legs, and one horse 
how many legs have one 
ox and one horse ? How 
many are 4 and 4 ? 

If a horse will eat 5 quarts of meal, and an 
ox 4 quarts, how many quarts of meal will a 
horse and an ox eat ?• 

How many are 5 and 4 ? 4 and 5 ? 

An ox will eat 3 tons of hay in a year, and a 
horse 5 tons; how many tons will an ox and a 
horse together eat ? ■ 











PRIMARY ARITHMETIC. 


36 


LESSON XXII. 


Repeat the following tables : 


1 

and 

1 

are 

9 

2 

and 

1 

are 

3 

2 

and 

1 

are 

3 

2 

and 

2 

are 

4 

3 

and 

1 

are 

4 

2 

and 

3 

are 

5 

4 

and 

1 

are 

5 

2 

and 

4 

are 

6 

5 

and 

1 

are 

6 

2 

and 

5 

are 

7 

6 

and 

1 

are 

7 

2 

and 

6 

are 

8 

7 

and 

1 

are 

8 

2 

and 

7 

are 

9 

8 

and 

1 

are 

9 

2 

and 

8 

are 

10 

9 

and 

1 

are 

10 

2 

and 

9 

are 

11 

10 

and 

1 

are 

11 

2 

and 

10 

are 

12 

3 

and 

1 

are 

4 

1 

and 

4 

are 

5 

3 

and 

2 

are 

5 

2 

and 

4 

are 

6 

3 

and 

3 

are 

6 

o 

O 

and 

4 

are 

7 

3 

and 

4 

are 

7 

4 

and 

4 

are 

8 

3 

and 

5 

are 

8 

5 

and 

4 

are 

9 

3 

and 

6 

are 

9 

6 

and 

4 

are 

10 

3 

and 

7 

are 

10 

7 

and 

4 

are 

11 

3 

and 

8 

are 

11 

8 

and 

4 

are 

12 

3 

and 

9 

are 

12 

9 

and 

4 

are 

13 

3 

and 

10 

are 

13 

10 

and 

4 

are 

14 

5 

and 

1 

are 

6 

5 

and 

6 

are 

11 

D 

and 

9 

are 

7 

5 

and 

7 

are 

12 

5 

and 

3 

are 

8 

5 

and 

8 

are 

13 

6 

and 

4 

are 

9 

5 

and 

9 

are 

14 

5 

and 

5 

are 

10 

5 

and 

10 

are 

15 


John has T cents, and James has 6; how 
many cents have they together? 










PRIMARY ARITHMETIC. 

37 


LESSON 

XXIII. 


Repeat the following tables: 


1 from 

1 leaves 

0 

2 from 2 leaves 

0 

1 from 

2 leaves 

1 

2 from 3 leaves 

1 

1 from 

3 leaves 

2 

2 from 4 leaves 

2 

1 from 

4 leaves 

3 

2 from 5 leaves 

3 

1 from 

5 leaves 

4 

2 from 6 leaves 

4 

1 from 

6 leaves 

5 

2 from 7 leaves 

5 

1 from 

7 leaves 

G 

2 from 8 leaves 

G 

1 from 

8 leaves 

7 

2 from 9 leaves 

7 

1 from 

9 leaves 

8 

2 from 10 leaves 

8 

1 from 10 leaves 

9 

2 from 11 leaves 

9 

3 from 

3 leaves 

0 

4 from 4 leaves 

0 

3 from 

4 leaves 

1 

4 from 5 leaves 

1 

3 from 

5 leaves 

2 

4 from 6 leaves 

2 

3 from 

6 leaves 

3 

4 from 7 leaves 

3 

3 from 

7 leaves 

4 

4 from 8 leaves 

4 

3 from 

8 leaves 

5 

4 from 9 leaves 

5 

3 from 

9 leaves 

6 

4 from 10 leaves 

6 

3 from 10 leaves 

7 

4 from 11 leaves 

< 

3 from 11 leaves 

8 

4 from 12 leaves 

8 

3 from 12 leaves 

9 

4 from 13 leaves 

9 

5 from 

5 leaves 

0 

5 from 10 leaves 

5 

5 from 

6 leaves 

1 

5 from 11 leaves 

6 

5 from 

7 leaves 

2 

5 from 12 leaves 

7 

5 from 

8 leaves 

3 

5 from 13 leaves 

8 

5 from 

9 leaves 

4 

5 from 14 leaves 

9 

5 boys from 14 boys leaves how many boys ? 

5 boys and 9 boys 

are 

how many boys ? 









PRIMARY ARITHMETIC. 


38 


LESSON XXIV. 


1. Mr. Flint paid 6 dollars for a clock, and 

2 dollars more for repairing it; how 
many dollars lias the clock cost him ? 
6 and 2 are how many ? 2 and 6 ? 

2. Charles studied 6 hours one day, and 5 
hours the next day; how many hours did he 
study in two days ? 

How many are 6 and 5 ? 6 and 3 ? 

3. Mr. Dean paid 6 dollars for a cord of oak 
wood, and 4 dollars for a cord of pine; how 
many dollars did he pay for the two cords ? 

How many are 6 and 4 ? 4 and 6 ? 

4. Mr. Dean cut his pine wood in 6 hours, 
and his oak in 7 hours ; in how many hours did 
he cut the pine and the oak wood ? 

How many are 6 and 7 ? 8 and 6 ? 

5. Mr. Smith bought one pig for 6 dollars, 
and another for 9 dollars; how many 
dollars did he pay for both pigs ? 

How many are 6 and 9 ? 9 and 5 ? 

6. Mr. Smith planted 6 acres of corn, and 3 
acres of potatoes ; how many acres did lie plant ? 

7. If a pound of pork is worth 6 cents, and 
a pound of beef 8 cents, how many cents are a 
pound of pork and a pound of beef worth ? 

Repeat the table: 




6 and 1 are 7 
6 and 2 are 8 
6 and 3 are 9 
6 and 4 are 10 
6 and 5 are 11 


6 and 6 are 12 
6 and 7 are 13 
6 and 8 are 14 
6 and 9 are 15 
6 and 10 are 16 








PRIMARY ARITHMETIC. 


39 

LESSON XXV. 


1. Samuel caught 7 fishes the first time he 
went angling, and 3 the second 
time ; how many * fishes did he 
catch ? 

7 and 3 are how many ? 7 and 5 ? 

2. Samuel sold all the fishes he caught the first 
day for 7 cents, and those lie caught the second 
day for 6 cents; how many cents did he receive 
for all of his fishes ? 

How many are 7 and 6 ? 6 and 7 ? 

Repeat the table: 



7 and 1 are 8 
7 and 2 are 9 
7 and 3 are 10 
7 and 4 are 11 
7 and 5 are 12 


7 and 6 are 13 
7 and 7 are 14 
7 and 8 are 15 
7 and 9 are 16 
7 and 10 are 17 


The Teacher will give you the names, and 
explain the uses of the signs in the following 
table. This and the above table mean exactly 
the same. The words in the first mean the 
same as the signs in the second. 


7 + 

1 = 

8 


7 + 

6 

= 

13 

7 + 

2 =• 

9 


7 + 

7 

— 

14 

7 + 

3 = 

10 


7 + 

8 


15 

7 + 

4 = 

11 


7 + 

9 

= 

16 

7 + 

5 = 

12 


7 + 

10 

= 

17 

How 

many 

are 

6 + 

7? 

8 

+ 

7? 

How 

many 

are 

5 + 

7? 

9 

+ 

7? 








PRIMARY ARITHMETIC. 


40 


LESSON XXVI. 


1. There were 8 elephants in one menagerie, 
and three in another; how many 
were there in both ? 

How many are 8 and 8 ? 3 and 8 ? 

2. Albert paid 8 cents for going into one 
menagerie, and T cents for going into the other; 
how many cents did he pay in all ? 

How many are 8 and 7 ? 8 and 5 ? 

3. One of the elephants carried 8 boys and 10 
girls upon his back ; how‘many children did he 
carry upon his back ? 

How many are 8 and 10 ? 8 and 6 ? 

Repeat the table: 



8 + 1 = 9 
8 + 2 = 10 
8+ 3 = 11 
8+ 4 = 12 
8+ 5 = 13 


8+ 6 = 14 
8+ 7 = 15 
8+ 8 = 16 
8+ 9 = 17 
8 + 10 — 18 


LESSON XXVII. 

1. One hunter killed 9 tigers, and another 
killed 4; how many did both of 
them kill ? 

How many are 9 and 4 ? 4 and 9 ? 

2. One of these hunters sold his tiger skins 
for 9 dollars, and the other for 7 dollars; how 
many dollars did they both receive ? 

3. Susan found 9 chestnuts under one tree 
and 10 under another tree ; how many nuts did 
she find ? 





PRIMARY ARITHMETIC. 


41 


How many are 9 and 

1? 

1 and 9 ? 

How many are 9 and 

2 ? 

2 and 9 ? 

How many are 9 and 

3 ? 

3 and 9 ? 

How many are 9 and 

4? 

4 and 9 ? 

How many are 9 and 

5.? 

5 and 9 ? 

How many are 9 and 

6? 

6 and 9 ? 

How many are 9 and 

7? 

7 and 9 ? 

How many are 9 and 

8? 

8 and 9 ? 

How many are 9 and 

9? 

9 and 9 ? 

How many are 9 and 10 ? 

10 and 9 ? 


LESSON XXVIII 


1. Walter bought one globe 



for 10 dollars, 
and another for 5 dollars; what did 
he pay for both globes ? 

How many are 10 and 5 ? 10 and 2? 

2. Walter found 10 islands marked 
on his best globe, and 7 on the other; how 
many did he find on both ? 

How many arc 10 and 7 ? 7 and 10 ? 

3. If the sun is up 10 hours one day and 10 
hours the next day, how many hours is the sun 
up in the two days ? 

How many are 10 and 10 ? 

Repeat the table : 


10 + 1 = 11 
+ 2 = 12 
+ 3 = 13 
+ 4 = 14 
+ 5 = 15 


10 

10 

10 

10 


10+ 6 = 16 
10+ 7 = 17 
10+ 8 = 18 
10+ 9 = 19 
10 + 10 = 20 


4* 









LESSON XXIX. 

A few days ago, we saw a liappy group of 
children at play in the yard. Here we see 
them in the school-room; but there are more 
here than we saw in front of the school-house. 
Sometimes children are kept in from recess, 
to punish them, and sometimes they stay in 
of their own accord, to study. These scholars 
look like very good children ; those in their 
seats are very still and studious, and those on 




















































PRIMARY ARITHMETIC. 


43 


the floor are very eager to recite ; so I think the 
teacher did not keep them in to punish them. 

1. Can you count the scholars that are stand¬ 
ing on the floor ? Ten girls and ten boys. 

How many are 10 and 10 ? 

2. Count the scholars in the back row of 
seats. Now count those in the front row. 

How many are there in both rows ? 

How many are 3 and 6 ? ’6 and 3 ? 

3. Count the caps on the upper row of hooks. 
How many are there ? How many hooks with¬ 
out caps ? 

How many are 7 and 4 ? 4 and 7 ? 

4. How many caps are there in the second 
row ? How many hooks without caps ? 

8 and 3 ‘are how many ? 3 and 8 ? 

5. How many caps in the lower row ? How 
many hooks without caps ? 

How many are 9 and 2 ? 2 and 9 ? 

6. There is one cap hanging on the end of 
the desk; how many caps can you see in the 
room ? 

How many are 9 and 8 and 7 and 1 ? 

7. There are 20 scholars on the floor, and 6 

in the front row of desks; how many are 20 
and 6 ? 6 and 20 ? 

8. How many are 20 and 6 and 3 J 20 and 

3 and 6 ? 6 and 20 and 3 ? 

9. If we count the scholars and the teacher, 
we shall find the whole number of persons in 
the room. How many are there ? 

How many are 20 and 6 and 3 and 1 ? 20 

and 9 and 1V 20 and 10 ? 











44 


PRIMARY ARITHMETIC. 


LESSOK XXX. 

1. Mr. Abbott bought G barrels of flour, and 
sold 2 of them; how many barrels 
had he left ? 

2 from 6 leaves how many? 4 

from 6 ? 

How many are 6 and 2 ? 6 and 4 ? 

2. Mr. Abbott paid 5 dollars a barrel for his 
flour, and sold it at 6 dollars; how many dol¬ 
lars did he gain on 1 barrel ? 

5 from G leaves how many ? 1 from G ? 

Repeat the table: 


G from G leaves 0 
6 from 7 leaves 1 
6 from 8 leaves 2 
6 from 9 leaves 3 
G from 10 leaves 4 


6 from 11 leaves 5 
6 from 12- leaves 6 
6 from 13 leaves 7 
6 from 14 leaves 8 
6 from 15 leaves 9 



LESSON XXXI. 

1. Mr. Astor sent 7 ships to India, but 6 of 
them were wrecked ; how many of 
them reached India in safety ? 

saMMr G from 7 leaves how many ? 1 

from 7 ?- 

How many are 6 and 1 ? 1 and G ? 

2. 7 passengers sailed in one of Mr. Astor’s 
ships, but 3 of them were lost on the passage; 
how many were saved ? 

7 less 3 are how many ? 7 less 4 ? 

How many are 3 and 7 ? 4 and 7 ? 






PRIMARY ARITHMETIC. 45 

Repeat the table: 

7 from 7 leaves 0 

7 from 8 leaves 1 

7 from 9 leaves 2 

7 from 10 leaves 3 

7 from 11 leaves 4 

7 from 12 leaves 5 

7 from 13 leaves 6 

7 from 14 leaves 7 

7 from 15 leaves 8 

7 from 16 leaves 9 

LESSON 

XXXII. 

1. Mr. Smith owned 8 houses, but he has 

sold 5 them ; how many has 

^ ie 110W • 

tKsBBSog: How many are 8 less 5 ? 8 less 3 ? 

2. Mr. Smith rents his best house for 8 dol¬ 
lars a month, and his poorest for 6 dollars; 
how many more dollars does he receive, each 
month, for one than for the other ? 

6 from 8 leaves how many ? 3 from 8 ? 

How many are 6 and 2 ? 2 and 6 ? 

Repeat the table: 

8 less 1 are 7 

8 less 2 are 6 

8 less 3 are 5 

8 less 4 are 4 

8 less 5 are 3 

8 less 6 are 2 

8 less 7 arc 1 

8 less 8 are 0 

The Teacher will ex 
following table: 

plain the signs in the 

8 — 1 = 7 

8 — 2 = 6 

8 — 3 = 5 

8 — 4 = 4 

8 — 5 = 3 

8 — 6 = 2 

8 — 7 = 1 

8 — 8 = 0 










PRIMARY ARITHMETIC. 


46 


LESSON XXXIII. 


1. In one rail-road train, running from An¬ 
dover to Boston, there are 9 cars, 
and in another train there are 4 
cars ; how many more cars in the 

first train than in the second ? 

How many are 9 less 4 ? 9 less 5 ? 

How many are 9 and 4 ? 9 and 5 ? 

2. Suppose one train stops 9 times in going 
from Andover to Boston, and the other only 3 
times, how many more times does one train 
stop than the other ? 

How many are 9 less 3 ? 9 less 6 ? 

3. Nine daily coaches run on one road, and 4 
on another ; how many less run on 
the second than on the first road ? 

4 are how many less than 9 ? 

4. One coach carries 9 passengers, and another 
carries 5; how many does one carry more than 
the other ? 

5 from 9 leaves how many ? 4 from 9 ? 

5. One coachman drives 9 miles in an hour, 
and another drives 8 miles in the same time ; 
how much farther does one coachman drive in 
an hour than the other ? 

9 are how many more than 8 ? 

Repeat the table: 




9 — 9=0 

10 — 9 = 1 

11 — 9 = 2 

12 — 9 = 3 

13 — 9 = 4 


14 — 9 = 5 

15 — 9 = 6 

16 — 9 = 7 

17 — 9 = 8 

18 — 9 = 9 













PRIMARY ARITHMETIC. 


47 


LESSON XXXIV. 

1. Tiie express-wagon went to the depot 


10 times on Monday, and only 7 
times on Tuesday; how many 
more times did it go oii Monday 



than on Tuesday ? 

How many are 10 less 7 ? 10 less 3 ? 

How many are 10 and 7 ? 10 and 3 ? 

2. The express-man carried 10 packages to 
one house and only 5 to another; how many 
less packages did he carry to the second house 
than to the first ? 

If 5 are taken from 10, how many will re¬ 
main ? 

How many are 10 less 5 ? 10 — 5 ? 

How many are 10 and 5 ? 10 —f- 5 ? 

3. Henry can skate 10 miles in an hour, 


and Philip but 8 ; how many more 
miles can Henry skate in an hour 
than Philip ? 



10 are how many more than 8 ? 

How many are 10 and 8 ? 8 and 10 ? 

4. The ice was 10 inches thick one day 
when Henry skated, and only 4 inches thick 
on another day ; how many inches thicker was 
it on one day than on the other ? 

Pepeat the table: 


-10 — 10 = 0 
11 — 10 = 1 
12 — 10 = 2 

13 — 10 = 3 

14 — 10 = 4 


15 — 10 = 5 

16 — 10 = 6 

17 — 10 = 7 

18 — 10 = 8 
19 — 10 = 9 










48 PRIMARY ARITHMETIC. 



LESSON XXXV. 


Mr. Day and his family are enjoying a pic¬ 
nic in the grove. They are all delighted with 
a ramble in the country, after living in the city 
for several months. The boys are coming with 
the fishes they have caught. Ada and Fanny 
are making wreaths of flowers, while nurse is 
holding little Hattie, and Emma is watching 
her father and mother as they prepare the din¬ 
ner, which they will all eat with good appetites. 

■ Fido expects a share. 














PRIMARY ARITHMETIC. 49 


1. Fido lias 4 feet, but Mr. Day has only 2; 
how many more feet has Fido than Mr. Day ? 

Two is how many less than four ? 

2. Two little girls sit on one side of the 
nurse, and one on the other; how many on 
both sides? 

How many more on one side than on the 
other ? 

How many are 2 and 1 ? 2 less 1 ? 

3. Mr. Day has 4 girls and 2 boys; how 
many children has Mr. Day ? How many more 
girls than boys ? 

How many are 4 and 2 ? 4 less 2 ? 

4. There are 2 boys, 4 girls, 2 women, and 1 
man in Mr. Day’s family; how many persons 
are there in the family ? 

5. Now if we count Fido as one of the fam¬ 
ily, how many are there in the family ? 

How many are 2 and 4 and 2 and 1 ? 2 and 

4 and 2 and 1, and 1 ? 

6. We see 3 small trees on the hill on one 
side of Mr. Day, and 6 on the other side; how 
many do we see on both sides? How many 
more on one side than on the other ? 

6 are how many more than 3 ? 

3 are how many less than 6 ? 

How many are 6 and 3 ? 3 and 6 ? 

7. How many trees do you see in the picture? 

How many are 1 and 6 and 3 ? 6 and 1 and 3 ? 

How many are 10 — 3? 10 — 6? 

8. Joseph caught 7 fishes, and Daniel caught 
12 ; how many did both of them catch ? 

How many are 12 -f- 7 ? 12 — 7? 


5 





PRIMARY ARITHMETIC. 


50 


LESSON XXXVI. 



1. 1 sled and 1 sled, or 2 times 1 sled, are 
how many sleds ? 

2 times 1 are liow many ? Once 2 ? 

Twice 1 are how many ? 1 and 1 ? 



2. If Frank should make 1 top each day, 
how many tops would he make in 3 days ? 

How many are 3 times 1 ? Once 3 ? 



3. If Lewis eats 1 apple at each recess, how 
many apples will he eat in 4 recesses ? 

How many are 4 times 1 ? Once 4 ? 



4. If 1 pear costs 1 cent, how many cents 
will 5 pears cost ? 

How many are 5 times 1 ? Once 5 ? 

Repeat the table: 


6 times 1 are 6 

7 times 1 are 7 

8 times 1 are 8 

9 times 1 are 9 
10 times 1 are 10 


Once 6 is 6 
Once 7 is 7 
Once 8 is 8 
Once 9 is 9 
Once 10 is 10 




PRIMARY ARITHMETIC. 


51 


LESSON XXXVII. 



1. One boy lias 2 hands; how many hands 
have two boys ? 

How many are 2 times 2 ? 2 and 2 ? 



2. One boy has 2 feet; how many feet have 
3 boys ? 

How many are 3 times 2 ? Twice 3 ? 



3. One goat has 2 horns; how many horns 
have 4 goats ? 

How many are 4 times 2 ? Twice 4 ? 



4. One wheelbarrow has 2 handles; how 
many handles have 5 wheelbarrows ? 

How many arc 5 times 2 ? Twice 5 ? 

Repeat the table: 


6 times 2 are 12 

7 times 2 are 14 

8 times 2 are 16 

9 times 2 are 18 
10 times 2 are 20 


Twice 6 are 12 
Twice 7 are 14 
Twice 8 are 16 
Twice 9 are 18 
Twice 10 are 20 





PRIMARY ARITHMETIC. 


52 


LESSON XXXVIII. 



1. Here are 3 grape leaves on one stem, and 
3 on another ; how many leaves on both ? 

How many are twice 3 ? 3 times 2 ? 



2. If 3 oak leaves grow upon 1 stem, how 
many leaves grow upon 3 stems ? 

How many are 3 times 3? 3 —|— 3 —f- 3 ? 




3. Walter plucked 4 twigs from a walnut 
tree, and found 3 leaves on each twig; how 
many leaves did he pluck ? 

How many are 4 times 3 ? 3 times 4 ? 



4. If 3 pine leaves grow from 1 bud, how 
many grow from 5 buds ? 

IIow many are 5 times 3 ? 3 times 5 ? 

Repeat the table: 


6 times 3 are 18 

7 times 3 are 21 

8 times 3 are 24 

9 times 3 are 27 
10 times 3 are 30 


3 times 6 are 18 
3 times 7 are 21 
3 times 8 are 24 
3 times 9 are 27 
3 times 10 are 30 







PRIMARY ARITHMETIC. 


53 


LESSON XXXIX. 



1. One elephant has 4 legs; how many legs 
have 2 elephants ? 

How many are 2 times 4 ? 4 times 2 ? 



2. If a tiger has 4 legs, how many legs have 
3 tigers ? 

How many are 3 times 4 ? 4 times 3 ? 



3. How many feet have 4 lions, if each lion 
has 4 feet ? 

How many are 4 times 4 ? 



4. A camel has 4 feet; how many feet have 
5 camels ? 

How many are 5 times 4 ? 4 times 5 ? 



5. One dog has 4 legs; how many legs have 
6 dogs ? 

How many are 6 times 4 ? 4 times 6 ? 


5* 










PRIMARY ARITHMETIC. 


54 


Repeat the table: 

7 times 4 are 28 

8 times 4 are 32 

9 times 4 are 36 
10 times 4 are 40 


4 times 7 are 28 
4 times 8 are 32 
4 times 9 are 36 
4 times 10 are 40 


LESSON XL. 



1. Now for a boat-race! 5 boys in 1 boat, 
and 5 in the other; how many boys in both 
boats ? 


How many are twice 5 ? 5 times 2 ? 

How many are 5 and 5? 2 + 2 + 2 + 2 

+ 2 ? 



2. See the pretty birds’ nests! 5 eggs in 
each nest; how many eggs in 3 nests ? 

How many are three times 5 ? 5 times 3 ? 

How many are 5 and 5 and 5? 5 + 5 -f- 5 ? 



3. Here are 4 castors, with 5 bottles in each 
castor ; how many bottles in all ? 

How many are 4 times 5 ? 5 times 4 ? 










PRIMARY ARITHMETIC. 


55 



4. See these 5 flower-vases with 5 beautiful 
blossoms in each vase. How many blossoms 
are there in all the vases ? 

5 times 5 are how many ? 



5. If one dove is worth 5 cents, how many 
cents are 6 doves worth ? 

How many are 6 times 5 ? 5 times 6 ? 

How many are 6 and 6 ? 6 less 5 ? 



6. Mr. Pierce sold 7 chairs, and received 5 
shillings for each chair; how many shillings 
did he receive for the 7 chairs ? 

How many are 7 times 5 ? 5 times 7 ? 

How many are 5 -j-5 + 5 + 5 5 -j- 5 

+ 5 ? 

Repeat the table: 


6 times 5 are 80 

7 times 5 are 35 

8 times 5 are 40 

9 times 5 are 45 
10 times 5 are 50 


5 times 6 are 30 
5 times 7 are 35 
5 times 8 are 40 
5 times 9 are 45 
5 times 10 are 50 




56 PRIMARY ARITHMETIC. 



LESSON XLI. 

Look at this lively scene. It is a farm-yard 
on a bright Spring morning. Mr. Brown and 
his hired man have yoked the oxen, and are 
going to plow. Two of the boys are going to 
the field with the horse-cart, and the other two 
are driving the cows to pasture. Old Towser 
capers before the horse, and the biddies and the 
birds are as busy as he. 

Now for a lesson from the picture. 

1. Two boys are in the cart, and two are 










PRIMARY ARITHMETIC. 57 


driving the cows; how many boys are there in 
the picture ? 

How many are 2 and 2 ? 2 times 2 ? 

2. If we count Mr. Brown and his man, we 
have two more persons ; how many are 3 times 
2 persons ? 

Which is most, 3 times 2, or 2 times 3 ? 

3. Each ox has 2 horns ; how many horns 
have 4 oxen ? 

How many are 4 times 2 ? Twice 4 ? 

4. 5 pairs of martins are flying towards the 
bird-house ; how many martins are there ? 

How many are 5 times 2 ? Twice 5 ? 

5. There are 3 posts under each end of the 
corn-barn ; how many under both ends ? 

Twice 3 are how many ? 3 times 2 ? 

6. One ox has 4 legs; how many legs have 

4 oxen ? 

How many are 4 times 4 ? 

7. There are 5 doves on the corn-barn, and 

5 on one of the large barns ; there are also 5 
at their windows, but they are in the shade, 
and we cannot see them very well. How many 
doves in all ? 

IIow many are 3 times 5 ? 5 times 3 ? 

8. The harrow has 5 rows of teeth, and 5 teeth 
in each row ; how many teeth has the harrow ? 

How many are 5 times 5 ? 

9. In that part of the fence which we see in 
front of the cows, there are 5 posts. The dis¬ 
tance from 1 post to the next we call a space or 
length of fence ; how many lengths of fence are 
there between the 5 posts ? 








58 


PRIMARY ARITHMETIC. 


LESSON X L11. 

1. If one apple costs 1 cent, how many cents 
will 6 apples cost ? 

jEgSi How many are 6 times 1 ? Once 6 ? 

2. Henry paid 2 cents for a pear ; how 
many cents would 6 pears cost at the same 
rate ? 

How many are 6 times 2 ? Twice 6 ? 

3. Sarah sold 6 oranges at 3 cents apiece; 
how many cents did she receive for the 
6 oranges ? 

How many are 6 times 3 ? 3 times 6 ? 

4. What is the cost of 6 lemons at 4 
cents for each ? 

How many are 6 times 4 ? 4 times 6 ? 4 X~6 ? 
Repeat the table: 


6 times 
6 times 
6 times 
6 times 
6 times 


5 are 30 

6 are 36 

7 are 42 

8 are 48 

9 are 54 


6 times 10 are 60 


5X6 = 80 
6x6 = 36 
7 x 6 = 42 
8X6 = 48 
9 X 6 = 54 
10 X 6 = 60 


The Teacher will name the signs, and explain their use. 


LESSON XLIII. 

1. If a cabinet-maker can make one table in 
a day, how many tables can he make 
y |Jr f ii in 7 days ? 

How many are 7 times 1 ? Once 7 ? 








PRIMARY ARITHMETIC. 


59 


2. If one table drawer has 2 knobs, bow many 
knobs have 7 table drawers ? 

How many are 7 times 2 ? Twice 7 ? 

3. If one clock costs 3 dollars, liow many 
dollars will 7 clocks cost ? 

7 times 3 are liow many ? 3 times 
7 ? 

4. One chair has 4 legs ; how many legs 
have 7 chairs ? 

7 times 4 are how many ? 4 times 7 ? 4x7? 
Repeat the table: 




7 times 5 are 35 
7 times 6 are 42 
7 times 7 are 49 
7 times 8 are 56 
7 times 9 are 63 
7 times 10 are 70 


5 X 7 = 35 

6 X 7 = 42 

7 x 7 = 49 

8 X 7 = 56 

9 X 7 = 63 
10 X 7 = 70 


LESSON XLIV. 

1. A hunter shot 1 bear each time he went 
out to hunt; how many bears did he 
shoot in going out 8 times ? 

How many are 8 times 1 ? Once 8 ? 

2. One bear has 2 ears; how many ears have 
8 bears ? 

How many are 8 times 2 ? Twice 8 ? 

3. If a stool has 3 legs, how many legs have 
^ 8 stools ? 

How many are 8 times 3 ? 3 times 8 ? 

4. If pussy should catch 4 squirrels 
each day, how many squirrels would she 
catch in 8 days ? 

8 times 4 are how many ? 4 times 8 ? 8x4? 







PRIMARY ARITHMETIC. 


60 


Repeat the table: 

8 times 5 are 40 
8 times 6 are 48 
8 times 7 are 56 
8 times 8 are 64 
8 times 9 are 72 
8 times 10 are 80 


5X8 = 40 
6X8 = 48 

7 x 8 = 56 

8 X 8 = 64 

9 X 8 = 72 

10 x 8 = 80 


LESSON XLV. 

1. If a pound of figs costs 1 shilling, how 
many shillings will 9 pounds 
cost ? 

How many are 9 times 1 ? 
Once 9 ? 

2. How many figs will 9 trees 
bear, if each tree bears 2 figs ? 

How many are 9 times 2 ? 
Twice 9 ? 

How many are 9 and 9 ? 2 

times 9 ? 

8. John caught 4 fishes each time he went to 
fish ; how many did he catch in 
going 9 times ? 

9 times 8 are how many ? 3 times 
9? 3x9? 9 + 9 + 9? 

4. If one pound of fish is worth 4 cents, how 
many cents are 9 pounds worth ? 

9 times 4 are how many ? 4 times 9 ? 

Repeat the table: 

9 times 5 are 45 5 X 9 = 45 

9 times 6 are 54 6 X 9 = 54 

9 times 7 are 63 7 X 9 = 63 









PRIMARY ARITHMETIC. 


61 


9 times 8 are 72 
9 times 9 are 81 
9 times 10 are 90 


8 X 9 = 72 

9 X 9 = 81 
10 X 9 = 90 


LESSON XLVI. 


1 If every little bird has 1 head, how many 
heads have 10 little birds? 
How many are 10 times 

1 ? Once 10 ? 

2. How many wings 

have 10 little birds, if 
each little bird has 2 
wings ? 

How many are 10 times 

2 ? Twice 10 ? 

How many arc 10 and 10 ? 10 -|- 10? 

3. If these little birds come to your window 
3 times every day, how many times will they 
come in 10 days ? 

10 times 3 are how many ? 3 times 10 ? 

4. If one sheep is worth 4 dollars, how many 
dollars are 10 sheep worth ? 

How many are 10 times 4 ? 4 times 10? 
How many are 10 and 10 and 10 and 10? 

Repeat the table: 




10 times 6 are 60 
10 times 7 are 70 
10 times 8 are 80 
10 times 9 are 90 
10 times 10 are 100 


6X10= 60 
7x10= 70 
8X10= 80 
9 X 10 = 90 
10 x 10 = 100 


How many figures does it take.to write one hun¬ 
dred ? What arc they ? How are they placed ? 








PRIMARY ARITHMETIC. 



lesson xlvii. 

Grandfather and grandmother have a Christ- 

Mko Pa Tu’ are R ,vil >g presents to the little 
oiks. I lie Christmas-tree is very pretty trim 

Td ,r h fl f SS a 'i d Strca '" CrS > P-Per l^ltcVns, 

and bags of candy. It bears something for 
every one of the children. They all enjoy the 
party very much. See grandma smile, as little 
JGsie reaches up for the horn of plenty which 
grandpa is giving to her. 























PRIMARY ARITHMETIC. 63 


1. How many children do you see at the left 
of Elsie ? How many at the right ? 

2. If there are 4 children at the left of Elsie, 
and 9 at the right, how many are there on both 
sides of her ? 

How many arc 4 and 9 ? 9 and 4 ? 

3. How many children are there in the pic 
ture ? Count them. 

How many are 4 and 9 and 1? 4 and 1 

and 9 ? 

4. If we count grandpa and grandma, how 
many persons do we see in the picture ? 

How many are 14 and 2 ? 2 and 14 ? 

5. If Elsie finds 8 white sugar-plums, and 8 
red ones in her horn of plenty, how many sugar¬ 
plums will she find in it ? 

How many are 8 and 8 ? Two times 8 ? 

6. If she finds 8 white sugar-plums, and 8 
red ones and 8 yellow ones, how many will she 
find in all ? 

How many are 8 and 8 and 8 ? 3 times 8 ? 

7. If 7 of these children go home at 7 o’clock, 
and the rest remain, how many will remain ? 

7 from 14 leaves how many ? 

How many are 7 and 7 ? Twice 7 ? 

8. If the 7 children who go home at 7 o’clock, 
receive 3 bags of candy apiece, how many bags 
of candy do they all receive ? 

How many arc 7 times 3 ? 3 times 7 ? 

9. If the 7 children who remain receive 5 
presents each, how many presents do they all 
receive ? 

How many are 7 times 5 ? 5 times 7 ? 









PRIMARY ARITHMETIC. 


64 


LESSON XLVIII. 



1. It takes 2 boots to make a pair of boots; 
how many pairs will 4 boots make ? 

How many times 2 are there in 4 ? 

How many shoes make a pair of shoes ? 



2. It takes 2 socks to make a pair of socks; 
how many pairs do 6 socks make ? 

How many times 2 in 6 ? 



3. Here are 8 skates; how many pairs are 
there ? 

8 are how many times 2 ? 

4 times 2 are how many ? . 



4. Ten mittens are how many pairs of mit¬ 
tens ? 

2 in 10 how many times ? 

Repeat the table: 


2 in 2, once 
2 in 4, twice 
2 in 6, 3 times 
2 in 8, 4 times 
2 in 10, 5 times 


2 in 12, 6 times 
2 in 14, T times 
2 in 16, 8 times 
2 in 18, 9 times 
2 in 20, 10 times 








PRIMARY ARITHMETIC. 


65 


LESSON X LIX. 



1. One ship has 3 masts ; how many ships 
will 6 masts supply ? 

3 in 6 how many times ? 2 in 6 ? 



2. If 1 stool has 3 legs, how many stools will 
have 9 legs ? 

3 in 9 how many times ? 



3. If a twig has 3 leaves, how many such 


twigs will have 12 leaves? 

How many times 3 are 12 ? 

How many are 4 times 3 ? 3 times 4 ? 



4. There are 3 cherries in 1 cluster; how 
many such clusters will 15 cherries make ? 

15 are how many times 3 ? How many times 5 ? 
Repeat the table: 


3 in 18, 6 times 
3 in 21, T times 
3 in 24, 8 times 
3 in 27, 9 times 
3 in 30, 10 times 


6 times 3 are 18 

7 times 3 are 21 

8 times 3 are 24 

9 times 3 are 27 
10 times 3 are 30 





PRIMARY ARITHMETIC. 


6G 


LESSON L. 



1. In 1 chest there are 4 drawers; how many 
chests will have 8 drawers ? 

4 in 8 how many times ? 



2. If 4 wheels are needed for 1 wagon, how 
many wagons will 12 wheels furnish ? 

How many times is 4 contained in 12 ? 

How many are 3 times 4? 4 + 4 + 4? 



3. Sixteen blades will be enough for how 
many knives, if 4 blades are put in each knife ? 
4 in 10 how many times ? 



4. How many forks will together have 20 
prongs, if each fork lias 4 prongs? 

How many times 4 in 20 ? 5 in 20 ? 

Repeat the table: 


4 in 24, 
4 in 28, 
4 in 32, 
4 in 36, 
4 in 40, 


6 times 

7 times 

8 times 

9 times 
0 times 


4 times 
4 times 
4 times 
4 times 
4 times 


6 are 24 

7 are 28 

8 are 32 

9 are 36 
0 are 40 













PRIMARY ARITHMETIC. 


67 


LESSON LI. 


1. Ten bottles will furnish how many castors, 
if each castor has 5 bottles ? 



2. If 1 bird’s nest has 5 eggs, how many 
birds’ nests will have 15 eggs ? 


3. The boys, when playing, made some rings, 
or circles, on the ground, and put 5 marbles in 
each ring. They put down 20 marbles; in how 
many rings did they place them ? 


4. Emily found some flowers, and each flower 
had 5 leaves, or petals. In all she found 25 
petals; how many flowers did she find ? 

Repeat the table: 

6 

7 

8 

9 

50 -r 5 = 10 

The Teacher will explain the signs. 


5 in 30, 

6 times 

30-!-5 = 

5 in 35, 

7 times 

35 + 5 = 

5 in 40, 

8 times 

40-^5 = 

5 in 45, 

9 times 

45 5 = 

5 in 50, 

10 times 

50 -r 5 = 




68 PRIMARY ARITHMETIC. 



LESSON LII. 

Winter lias come. Now for rare sports — 
skating, coasting, sleighing! How the snow 
comes up round the horses’ feet! Do you not 
think those little birds will freeze their toes ? 

See the boys and the girls, the men and the 
women on the ice, and in the sleigh! They 
look as though they acted on the motto — 
“ Work while you work, and play while you 
play.” Let us work awhile now, and by-and-by 
ive will have our play. 

































PRIMARY ARITHMETIC. 69 


1. Here are '2 little birds on the snow; how 
many times 1 bird ? 

1 in 2 how many times ? 

2. Near the centre of the picture we see 6 
boys drawing a sled; how many times 2 boys 
are drawing the sled ? How many times 3 boys 
are drawing the sled ? 

2 in 6 how many times ? 3 in 6 ? 

How many are 3 times 2 ? 2 times 3 ? 

3. Counting the 2 girls on the sled, there are 
8 persons with the sled ; how many times 2 per¬ 
sons are with the sled? How many times 4 
persons ? 

2 in 8 how many times ? 4 in 8 ? 

How many are 4 times 2 ? 2 times 4 ? 4 

and 4 ? 

4. Near the right side of the picture we sec 
5 skaters in one group, and 4 in another; how 
many skaters in both groups ? 

How many are 5 and 4 ? 4 and 5 ? 

How many times 3 in 9 ? 

5. A great way off in the picture we see some 
birds flying. They are so far off that they look 
like mere specks. Can you count them? 

Twice 5 are how many ? 5 and 5 ? 

10 are liow many times 5 ? How many 
times 2 ? 

6. Beyond the boys who are drawing the 
sled, we see 8 boys skating. Now, if we count 
those 8 boys, and the 8 persons with the sled, 
how many shall we count ? 

How many are 8 and 8 ? Twice 8 ? 

16 are how many times 1? 2? 4? 8? 16? 





TO PRIMARY ARITHMETIC. 


7. Farmer Bruce is carrying the scholars home 
from school; 9 scholars are in the sleigh with 
him, and 1 more is trying to get in. How many 
persons are there in the sleigh ? If each horse 
draws the same number of persons, how many 
does each horse draw ? 

How many times 5 make 10 ? How many 
times 2 ? 

8. If the boy with the satchel on his back 
gets in, how many people will there then be in 
the sleigh ? 

How many are 9 and 1 and 1 ? 11 — 2 ? 

9. An animal is a creature that lives, and 
breathes, and feels. Is a horse an animal? Yes. 
Why? Because he lives, and breathes, and 
feels. Is a man an animal ? Yes. Is a bird 
an animal ? Yes. There are 50 animals in 
the picture ; can you count them ? 

50 are how many times 2 ? 5 ? 10 ? 25 ? 50 ? 

LESSON L111. 

1. Alfred paid 60 cents for 6 doves; what 
did he pay for 1 dove ? 

6 in 60 how many 
times ? 10 in 60 ? 

2. When 6 silk hats 
cost 80 dollars, how 
many dollars does 1 
hat cost ?' 

6 in 80 how many times ? 3 in 30 ? 

3. When 1 yard of ribbon costs 6 shillings, 
how many yards may bo bought for 42 shillings? 





PRIMARY ARITHMETIC. 


71 


Repeat the table: 


6 in 30, 

5 times 

6 X 

5 = 30 

6 in 36, 

6 times 

6 X 

6 = 36 

6 in 42, 

7 times 

6 X 

7 = 42 

6 in 48, 

8 times 

6 X 

8 = 48 

6 in 54, 

9 times 

6 X 

9 = 54 

6 in 60, 

10 times 

6 X 

10 = 60 


LESSON 

LIV. 




1 . When 1 cluster of grapes costs 7 cents, how 
many clusters can I buy for 35 cents ? 

7 in 35 how many times ? 5 in 35 ? 

2. If 7 clusters of grapes are worth 
63 cents, what is the value of 1 cluster ? 
7 in 63 how many times ? 7 in 49 ? 

How many are 7 times 9 ? 9 times 7 ? 

3. If 7 gallons of wine are worth 28 dollars, 
how many dollars is 1 gallon worth ? 

7 in 28 how many times? 7 in 70 ? 

How many are 10 times 7 ? 4 times 7 ? 
Repeat the table: 


7 

in 

7, 

once 

7 - 

-7 = 

1 

7 

in 

14, 

twice 

14- 

-7 = 

2 

7 

in 

21, 

3 times 

21 - 

-7 = 

3 

7 

in 

28, 

4 times 

28 - 

-7 = 

4 

7 

in 

35, 

5 times 

35 - 

- 7 = 

5 

7 

in 

42, 

6 times 

42 - 

-7 = 

6 

7 

in 

49, 

7 times 

49 - 

- 7 = 

7 

7 

in 

56, 

8 times 

56 - 

-7 = 

8 

7 

in 

63, 

9 times 

63 - 

- 7 = 

9 

7 

in 

70, 10 times 

70 - 

- 7 = 

10 






72 


PRIMARY ARITHMETIC. 


LESSON LV. 

1. If it costs 8 dollars to paint a portrait, 
how many portraits may be painted 
for 40 dollars ? 

8 in 40 how many times ? 8 in 56 ? 

2. If 8 photographs cost 16 dollars, what is 
the cost of 1 photograph ? 

8 in 16 how many times ? 2 in 16 ? 

How many are 2 times 8 ? 9 times 8 ? 

3. If 48 dollars are paid for 8 pairs of ear¬ 
rings, what is the price of 1 pair ? 

8 in 48 how many times ? 8 in 80 ? 

How many are 8 times 8 ? 7 times 8 ? 


Repeat the table: 


8 in 40, 5 times 

40 ~ 8= 5 

8 in 48, 6 times 

48 -T- 8= 6 

8 in 56, 7 times 

56 -f- 8 = 7 

8 in 64, 8 times 

6 4 "t- 8 = 8 

8 in 72, 9 times 

72 -r- 8 = 9 

8 in 80, 10 times 

80 -T- 8 = 10 

LESSON 

LVI. 


1. Nine boys have 18 hands; how many hands 
has 1 boy ? 

9 in 18 how many times ? 2 in 18 ? 

2. Nine boys have 72 fingers; how many 
fingers has 1 boy ? 

9 in 72 how many times ? 9 in 27 ? 

72 -f- 9 = how many ? 3x9? 3 + 9? 










PRIMARY ARITHMETIC. 


73 


3. How many fig-trees will bear 81 pounds 
of figs, if each tree bears 9 pounds ? 

9 in 81 how many times ? 9 in 90 ? 
How many are 9 -f* 9 ? 18 — 9? 
Repeat the table: 


9 in 45, 
9 in 54, 
9 in 63, 
9 in 72, 
9 in 81, 


5 times 

6 times 

7 times 

8 times 

9 times 


9 in 90, 10 times 


45^9= 5 
54 -f-9= 6 
63-^9= 7 
72 ^ 9 = 8 
81 -5- 9 = 9 
90 -v- 9 = 10 



LESSON L V11. 

1. If 10 chickens are worth 30 shillings, how 
many shillings is 1 chicken worth ? 

10 in 30 how many times? 3 
in 30 ? 

2. Ten pounds of poultry are worth 90 cents; 
what is 1 pound worth ? 

10 in 90 how many times ? 9 in 90 ? 

3. If 10 pairs of gloves cost 80 shillings, how 
many shillings will pay for 1 pair ? 

10 in 80 how many times? 10 in 60? 

How many are 10 -f- 5 ? 10 —J— 5 ? 

Repeat the table: 


10 in 

50, 

5 times 

10 X 

5= 50 

10 in 

60, 

times 

10 X 

6= 60 

10 in 

70, 

7 times 

10 X 

7= 70 

10 in 

80, 

8 times 

10 X 

8 = 80 

10 in 

90, 

9 times 

10 X 

9 = 90 

10 in 

100, 

10 times 

10 X 10 = 100 


7 




PRIMARY ARITHMETIC. 



LESSON L VIII. 


Tins great ship is almost ready to start on a 
°ng voyage across the wide ocean. A great 
many ships are gone several years on a siimle 
voyage. Some of them go round the world 
and some go to distant ports, and then return. ’ 
. , 18 slll P> tlie Ocean Queen , lies at anchor 

m deep water, a short distance from the shore 
and a great many people have left the shore in 
small boats, to get on board and sail in her. 




























PRIMARY ARITHMETIC. 75 


There is a man standing up in the nearest 
boat, and waving his handkerchief. Perhaps he 
is bidding good-by to his friends on shore. In 
the next boat there is a flag flying in the wind 
at the stern of the boat. 

1. You may count the folks in the boat where 
the little flag is flying. How many are there ? 10. 

How many times 2 ? How many times 5 ? 

2. In two boats there are twice as many peo¬ 
ple as in 1; how many are there in 2 boats ? 

2 times 10 are how many ? 10 and 10 ? 

20 are how many times 2? 4? 5? 10? 

3. In the nearest boat we see 3 oars, which 
the sailors are using to row the boat to the ship. 
They are also using 3 more oars on the other 
side, but we cannot see them; how many oars 
are they using ? 

6 are how many times 3 ? How many times 2 ? 

4. The boat near the right side of the picture 
also has 6 oars ; how many oars have both boats ? 

How many are 6 and 6 ? Twice 6 ? 

12 are how many times 1? 2? 3? 4? 

6 ? 12 ? 

5. In the boat that has the flag there are 8 
oars; how many oars in that boat and the one 
this side of it ? 

How many are 8 and 6 ? 8 less 6 ? 

14 are how many times 2? 7? 14? 1? 

6. There are 10 persons in eacli boat; how 
many persons are there in 3 boats ? 

30 are how many times 3? 5? 6? 10? 

7. Ten men in each boat, how many in 4 
boats ? 





PRIMARY ARITHMETIC. 


76 


How many are 4 times 10 ? 10 times 4 ? 

40 are how many times 4? 5? 8? 10? 

20 ? 2 ? 

8. If there are 10 men in each boat, how 
many boats contain 50 men ? 

50 is how many times 5 ? 10 ? 25 ? 2 ? 

9. If there are 10 men in each boat, how 
many men are there in 6 boats ? in 7 boats ? in 
8 boats ? in 9 boats ? in 10 boats ? 

How many are 10 x 6 ? 10 X 7 ? 10x8? 
10X9? 10x10? 


LESSON LIX. 

1. How many are 2 and 8? 2 and 5? 2 

and 7 ? 2 and 9 ? 

2. How many are 3 and 4 ? 3 and 6 ? 3 

and 8 ? 3 and 10 ? 

3. How many are 4 + 3 ? 4 -j— 4 ? 4 -f- 7 ? 

4 + 9? 

4. How many are 5 + 2? 5 + 7? 5 + 5? 

5 + 10? 

5. How many are 6 and 3 ? 6 and 6 ? 6 

and 5 ? 6 and 8 ? 

6. How many arc 7 and 1 ? 7 and 6 ? 7 

and 9 ? 7 and 10 ? 

7. How many are 8 and 4 ? 8 and 2 ? 8 

and 6 ? 8 and 9 ? 

8. How many are 9 + 3? 9 + 6? 9 + 4? 

9 + 10 ? 

9. How many are 10 + 4 ? 10 + 6 ? 10 
+ 7 ? 10 + 10? 

10. How many are 3 and 5 ? 4 and 9 ? 8 

and 4 ? 6 and 10 ? 





PRIMARY ARITHMETIC* 77 


11. How many are 7 and 2? 6 and 3? 8 

and 1 ? 5 and 4 ? 

12. How many are 3 and 2 and 7 ? 4 and 6 

and 8 ? 3 and 7 ? 

13. How many are 4 —2 6 —2 ? 7 + 1 

-f- 5 + 3 ? 

14. How many are 3 + 2 + 5+ 2? 4 + 6 

+ 7 + 2? 

15. How many are 1 and 6 and 5 ? 9 and 3 ? 

LESSON LX. 

1. If 1 orange costs 3 cents, how many cents 
will 4 oranges cost? Ans. 12 cents. Why? 
Aas. 4 oranges will cost 4 times as many cents 
as 1 orange ; therefore, if 1 orange costs 3 
cents, 4 oranges will cost 4 times 3 cents, which 
are 12 cents. 

2. If 1 coat is worth 10 dollars, what are 7 
coats worth ? Why ? 

3. If Louisa spells 9 words at each lesson, 
how many words will she spell in 9 lessons ? 
Why ? 

4. How many are 7 less 4 ? 6 less 5 ? 

5. How many are 8 — 4? 9 — 3? 10 — 7? 

6. One steamboat sails 12 miles in an hour, 
and another sails 10 miles in an hour; how 
much farther does one sail than the other ? 
Ans. 2 miles. Why ? Ans. It is just as true 
that 10 miles taken from 12 miles leaves 2 miles, 
as that 10 taken from 12 leaves 2. 

7. One apple-tree bears 10 barrels of apples, j 
and another only 7 barrels ; how many barrels ! 
less does one tree bear than the other ? Why ? j 


7 * 









PRIMARY ARITHMETIC. 


78 


LESSON LX I. 

1. If this pretty nightingale should sing 9 
hours to-night, and 7 
hours to-morrow night, 
how many hours would 
it sing in the two 
nights ? 

2. Some blackbirds 
are sitting on a tree, 
10 on one branch and 
10 on another ; how 
many blackbirds are on both branches ? 

3. Seven boys and 8 girls are playing blind- 
man’s-buff ; how many children are at play ? 

4. There are 10 rounds in one ladder, 8 in 
another, and 9 in another; how many rounds 
are there in the three ladders ? 

5. Willie has 10 hens, 6 turkeys, and 8 geese; 
how many fowls has he ? 

6. John bought a coat for 10 dollars, a hat 
for 5 dollars, and a pair of boots for 4 dollars; 
how many dollars did he pay for all ? 

7. Mary’s writing-book cost 7 cents, and her 
pen-holder 2 cents ; what did both cost ? 

How many more cents did the writing-book 
cost than the pen-holder ? 

8. A farmer sold 5 cows to one man, and 4 
to another, and then had 10 remaining; how 
many cows had he at first ? How many more 
had he remaining than he sold ? 

9. How many are 10 less 5 ? 10 less 4 ? 

10. How many are 7 — 3? 8 — 6? 12 — 

4 ? 10 — 7? 6 — 3? 9 — 8? 9 — 1 ? 










PRIMARY ARITHMETIC. 


79 


11. How many are 11 — 6? 11 — 5 ? 9 
■— 6 ? 9 — 3? 7 — 5? 7 — 2? 8—5? 
8 — 3? 

12. 7 from 9 leaves how many ? 7 from 11 ? 

7 from 15 ? 7 from 12 ? 7 from 18 ? 

13. 8 from 11 leaves how many ? 8 from 18 ? 

8 from 16 ? 8 from 20 ? 8 from 12 ? 


LESSON LX11. 



1. Robert caught one codfish that weighed 
15 pounds, and another that weighed 7 pounds ; 
what did they both weigh ? How much did one 
weigh more than the other ? 

2. Edwin paid 5 dollars for a plow, 3 dollars 
for a wheelbarrow, and had 7 dollars left; how 
many dollars had he at first ? 

3. Henry had no money, but he sold 5 mar¬ 
bles for 10 cents, and a top for 12 cents, and 
then he bought a knife for 15 cents ; how many 
cents had he left ? 

4. Addie found 12 apples under a tree; but 
she ate 2 of them, and gave 3 to Mary and 4 to 
Willie ; how many had she then ? 

5. Four years ago Willie was 10 years old; 
how old is he now ? 

6. Sarah is 13 years old; how old was she 6 

years ago ? j 










80 PRIMARY ARITHMETIC. 


7. From Andover to Lowell is 9 miles, and 
from Andover to Lawrence 4 miles ; how much 
farther is it to Lowell than to Lawrence ? 

8. Albert caught 7 gray squirrels and 6 red 
squirrels. He lost 5 of the gray ones and 3 of 
the red ones ; how many squirrels had he then ? 

9. In a bucket there were 20 pounds of sugar; 
but 6 pounds were used one day and 5 pounds 
the next day ; how many pounds were left ? 

10. A horse ate 4 tons of hay, a pair of oxen 
6 tons, and three cows 5 tons; how many tons 
did they all eat ? 

11. Daniel picked 12 quarts of chestnuts, and 
James 8 quarts; how many quarts did they 
both pick ? 

12. Georgie is now 4 years old ; in how many 
years will he be 10 years old ? 

18. Mary’s father and mother together gave 
her 13 cents ; her father gave her 9 cents ; how 
many cents did her mother give her ? 

14. Mr. Smith owed me 17 dollars, but he 
has paid 10 dollars ; how many dollars does he 
still owe me ? 

15. Two numbers, taken together, make 14; 
one of them is 4 ; wliat is the other ? 

16. Three numbers, taken together, make 17; 
the first is 8, the second is 4 ; what is the third ? 

17. David has 20 marbles. Twelve of them 
are in his pocket, and the rest in his hand ; how 
many are in his hand ? 

18. Lucy had 12 cents. She bought a lemon 
for 4 cents, and an orange for 6 cents, and then 
found 3 cents ; how much money had she then ? 




PRIMARY ARITHMETIC. 



LESSON L X111. 


1. The Antelope is a beautiful but timid crea¬ 


ture. How far would 
he run in 9 hours, if he 



* (J p ran 10 miles each hour? 
M&f, 2. A sportsman took 
45 antelopes in 5 days, 
• taking the same number 
each day ; how many 


did he take each day ? 


3. How many lemons, at 3 cents each, can be 
bought for 15 cents ? Why 5 ? Am. As many 
times as 3 cents are contained in 15 cents, so 
many lemons may be bought; 3 cents are con¬ 
tained 5 times in 15 cents ; therefore 5 lemons, 
at 3 cents each, may be bought for 15 cents. 

4. How many oranges, at 4 cents each, may 
be bought for 36 cents ? Why ? 

5. When cloth is worth 5 dollars a yard, how 
many yards can be bought for 35 dollars ? Why ? 

6. If 28 oranges are divided equally between 
7 boys, how many will each boy receive ? Why ? 

7. Julia has 6 pictures, and Emily has 7 times 
as many ; how many has Emily ? 

8. How many are 8 times 3 ? 3 times C ? 5 
times 7 ? 7 times 9 ? 4 times 10 ? 

9. How many are 6 times 9 ? 9 times 9 ? 8 

times 6 ? 8 times 8 ? 8 times 7 ? 


10. How many are 10 X 5? 6x10? 9x4? 

4X9? 8X2? 6X5? 7x6? 

11. How many are 5 times 8 ? 8 times 5 ? 9 

times 8 ? 10 times 10? 11 times 10 ? 









82 


PRIMARY ARITHMETIC. 


LESSON LX IV. 

I. If 1 balloon will carry np 9 persons, how 
many balloons will 
it take to carry up 
68 persons ? Why ? 

2. One balloon was 
up 7 hours at one 
time, and another 
was up 6 times as 
long ; how long was 
the second balloon 
up ? Why ? 

3. If 2 oranges are worth as much as 4 lem¬ 
ons, how many oranges will pay for 12 lemons ? 

4. Mr. Holt bought 2 barrels of flour at 10 
dollars a barrel, and paid for it with cloth at 4 
dollars a yard; how many yards did it take ? 

5. Arthur bought 4 tops at 6 cents apiece, and 
paid for them with marbles at 2 cents apiece; 
how many marbles did it take ? Why ? 

6. How many times 2 in 6 ? in 10 ? in 16 ? 
in 8 ? in 20 ? in 18 ? in 14 ? 

7. How many times 5 in 15 ? in 25 ? in 50 ? 
in 35 ? in 10 ? in 45 ? 

8. How many are 12-4-3? 18-4-3? 27 

-4- 3 ? 15 4- 3 ? 30 4- 3? 9 4-3? 214-3? 

9. How many are 48 4- 6 ? 24 — 6 ? 60 

4- 6 ? 6 4-6? 54 4- 6? 36-4-6?* 

10. Twenty are how many times 4 ? How 

many times 5? 10? 2? 20? 1? 

II. Twenty-four are how many times 6 ? 3 ? 

8? 4? 12? 2? 24? 1? 










PRIMARY ARITHMETIC. 83 


LESSON LXV. 

1. If 6 oranges cost 24 cents, how many cents 
will 8 oranges cost ? Why ? 

2. 6 in 24 how many times ? 4 in 24 ? 

3. 8 times 4 are how many ? 4 times 8 ? 

4. If a horse travels 15 miles in 3 hours, how 
far will he travel in 7 hours ? Why ? 

5. If 3 barrels of apples cost 9 dollars, how 
many barrels may be bought for 15 dollars ? 

G. How many apples, at 2 cents apiece, must 
be given for 8 oranges, at 3 cents apiece ? Why ? 

7. 8 times 3 are how many times 2 ? 

8. How many tons of hay, at 10 dollars a 
ton, will pay for 5 barrels of flour, at 6 dollars 
a barrel ? Why ? 

9. 6 times 5 are how many times 10 ? 

10. 5 times 3 are how many times 5 ? 

11. 3 times 5 are how many times 3 ? 

12. 5 lemons, at 3 cents apiece, will pay for 
how many oranges, at 5 cents apiece ? 

13. 3 oranges, at 5 cents apiece, will pay for 
how many lemons, at 3 cents apiece ? 

14. Forty are how many times 8 ? 4 ? 10 ? 

5? 2? 20? 40? 1? 

15. Thirty are how many times 3 ? 6 ? 5 ? 

10? 2? 15? 30? 1? 

16. Thirty-six are how many times 6 ? 9 ? 

12?' 3? 4? 36? 1? 

17. Eighteen are how many times 3 ? 9 ? 

6? 2? 18? 1? 

18. Forty-eight are how many times 6 ? 12 ? 
4 ? 8 ? 48 ? 1 ? 








84 PRIMARY ARITHMETIC. 



LESSON LXVI. 


Teacher. Ella is just cutting that nice great 
apple into two equal parts. What do you call 
one of the parts ? 

Pupil. It is one half of an apple. 

T. That is right. How many halves of an 
apple make a whole apple ? 

P. Two. 

T. Right. Suppose it was a pear that Ella 
was cutting into two equal parts, what would 
one of the parts be ? 

P. It would be one half of a pear. 

T. How many halves of a pear make a whole 
pear ? 

P. Two. 

T. Do two halves of a dollar make a whole 
dollar ? 

P. Yes. Two halves of any thing make the 
I whole of that thing. 












PRIMARY ARITHMETIC. 85 

T. Very well. Arthur has just cut another 
apple into three equal parts. What do you call 
one of those parts ? 

P. It is one third of an apple. 

T. What do you call two of the parts ? 

P. Two of the parts are two thirds of an apple. 

T. How many thirds of an apple make a 
whole apple ? 

P. Three. 

T. Do three thirds of a pear make a whole 
pear ? 

P. They do. Three thirds of any object make 
the whole of that object. 

T. There is another apple on the middle of 
the table, which has been cut into four equal 
parts. Wliat are those parts ? 

P. One of the parts is one fourth of an apple; 
two of the parts are two fourths; three of the 
parts are three fourths; and the four parts are 
four fourths of an apple. 

T. How many fourths of an apple make a 
whole apple ? 

P. Four. And four fourths of a pear make a 
whole pear ; and four fourths of a dollar , or four 
quarters of a dollar , make a whole dollar. 

T. Very well indeed. On this side of the 
table there are two loaves of cake. The loaf 
nearest Ella is cut into five equal parts, and we 
call the parts fifths; one part is one fifth; two 
parts are two fifths; three parts are three fifths , 
and so on. 

The other loaf is cut into six equal parts, and 
the parts are called sixths. 


s 








PRIMARY ARITHMETIC. 


86 


LESSON L XV11. 

1. When a pie is cut or divided into 7 equal 
parts, what is one of those parts called ? 

2. What are two of the parts called ? Ans 
Two sevenths of the pie. 

8. What are five of the parts called ? 

4. How many sevenths of a thing make the 
whole thing ? Ans . Seven. 

5. When a thing is divided into 8 equal parts, 
what is one of the parts called ? 

6. What are three of the parts called ? 

7. How many eighths make a whole one ? 

8. What is meant by one ninth of a thing? 
Ans. One of the 9 equal parts into which that 
tiling is divided. 

9. What is meant by 7 ninths of a thing? 
Ans. Seven of the 9 equal parts into which the 
thing is divided. 

10. How many ninths make a whole one ? 

11. What is meant by one tenth of a thing? 

12. How many tenths make a whole one ? 

18. Mary had 8 tenths of a dollar, and found 

another tenth ; how many tenths of a dollar 
had she then ? 

14. 3 tenths and 1 tenth are how many 
tenths ? 

15. John planted 2 sevenths of an acre with 
beans, and 8 sevenths with corn; what part of 
an acre did lie plant with both ? 

16. Edwin worked 1 fourth of the day in the 
garden, and 2 fourths in the field ; what part 
of the day did he work in both ? How much 

! __ 








PRIMARY ARITHMETIC. 87 


longer did he work in the field than in the 
garden ? 

17. Ezra bought an Algebra for 3 fourths of 
a dollar and sold it for 2 fourths; did he gain or 
lose by his bargains ? How much ? 

18. Willie gave 2 eighths of an orange to his 
sister, and 5 eighths to his brother; what part 
of the orange did he give away ? How much 
more to his brother than to his sister ? What 
part of the orange did he keep for himself? 

19. Two eighths and 5 eighths are how many 
eighths ? 

20. Five eighths less 2 eighths are how many 
eighths ? 

21. Mr. Hall spent 4 tenths of his life in 
Boston, and 3 tenths in New York; what part 
of his life did he spend in the two cities ? 

22. Mr. Jones spent 1 fifth of his money in 
one year, and 3 fifths the next year; what part 
of his money did he spend in 2 years ? What 
part had he then remaining ? 

23. 1 fifth and 3 fifths are how many fifths ? 

24. How many fifths remain if 4 fifths are 
taken from 5 fifths ? 

25. Mr. Abbott spent 2 sixths of a day in 
Miss Choate’s school, 1 sixth in Miss Fay’s, and 
the remainder of the day in his own ; what 
part of the day was he in his own school ? 

26. 2 sixths and 1 sixth taken from 6 sixths 
leave how many sixths ? 

27. If a box of strawberries cost 3 tenths of 
a dollar, a pineapple 2 tenths, and a melon 4 
tenths, what part of a dollar did they all cost? 









88 PRIMARY ARITHMETIC. 


LESSON LXVIII. 

When anything is divided into any number 1 
of equal parts, what are the parts called ?’ 

Ans. Each part is called a fraction of the 
thing that is divided into parts. 

We use two numbers to write a fraction; thus, 
we write one half in this way: l ; one third in this 
way: £; two thirds in this way: §; one fourth 
in this way : j ; three fourths in this way : j. 

In each fraction there are two numbers , one 
over the other, with a line between them. The 
number below the line tells how many equal 
parts the thing is divided into, and the number 
above the line tells how many of the parts we 
are talking about. 

1. Into how many equal parts is the loaf of 
cake near Ella divided ? Ans. 5. 

2. What is the fraction that stands for one of 
these 5 parts ? Ans. 4 . 

8. What fraction stands for 2 of the parts ? 
Ans. §. For 8 parts ? f. For 4 parts ? 

4. If a thing is divided into 6 equal parts, 
what fraction stands for, or represents, 1 of the 
parts ? Ans. £. 

5. What fraction represents 2 of the parts ? 
f. 8 parts? f. 4 parts? 5 parts? 

6. The apple on the middle of the table was 
first cut into two halves, and then each half was 
cut into two equal parts ; what is one of these 
small parts ? Ans. It is £ of an apple. 

7. Then 4 is the same as how many fourths? 
Ajis. I is the same as f. 









PRIMARY ARITHMETIC. 89 


8. The cake at the right side of the table was 
first cut into three equal parts, or thirds , where 
you see the large dark lines. Then each of 



these thirds was cut into two equal parts ; so 
we see that the whole cake is cut into 6 parts, 
and each part is £ of the cake. We also see 
that £ of the cake is the same as § of the cake. 

9. Is J of a pear the same as § of a pear? 
Ans . It is; J of anything is equal to § of the 
same thing. 

LESSON LX I X. 

1. In one apple there are 2 halves; how 
many halves arc there in 8 apples ? Why 6 ? 
Ans . Since there are 2 halves in 1 apple, there 
are 3 times 2 halves, which are 6 halves, in 3 
| apples. 

) 2. What fraction represents 6 halves ? Ans. |. 


8 * 



















90 PRIMARY ARITHMETIC. 


3. How many fourths of a dollar in 2 dollars? 
Why ? 

4. How many fourths of an apple in 3 apples ? 
In 4 apples ? In 5 apples ? In 6 apples ? Why ? 

5. If | of a barrel of flour costs 5 dollars, 
how many dollars do 2 halves, or a whole bar¬ 
rel, cost ? Why ? Ans. Since \ of a barrel 
costs 5 dollars, 2 halves cost twice 5 dollars. 

6. If ^ of a yard of cloth is worth 2 dollars, 
what is a whole yard worth ? Why ? 

7. Two is £ of what number ? Why 6 ? Ans. 
Since 2 is one third of the number, three thirds, 
or the' whole of the number, will be 3 times 2. 

8. Mr. Phillips had 12 sheep in a pasture, 
but a large dog drove 
h of them out; how 
many sheep did he 
drive out ? How many 
thirds of the flock re¬ 
mained in the pas¬ 
ture ? How many 
sheep? How many 
thirds are § less & ? 

9. Four is J of what number? Why? 

10. Eight is § of what number ? Why ? Ans. 
Since 8 is §, ^ of 8, which is 4, is £; and since 
4 is £, §, or the whole, will be 3 times 4, which 
are 12. 

11. If £ of a melon costs 5 cents, what will 
I a whole melon cost ? Why ? 

12. 5 is ^ of what number? Why? 

13. 4 is 1 of what number? Why ? 

14. Martha lost 5 cents, which was of all 1 











PRIMARY ARITHMETIC. 91 


the money she had; how much money had 
she ? 

15. 5 is 1of what number? Why? 

16. 10 is 4 of what number ? Why ? 

17. If 4 of an acre of land is worth 9 dollars, 
what are | of an acre worth ? Why ? 

What are § worth ? 4 ? £ ? f ? Why ? 

18. 9 is £ of what number? 

19. If 18 is £ of some number, what is 4 of 

the same number? Why? What is £ of the 
same number ? £ ? £ ? Wliy ? 

20. If 4 of a yard of clotb costs 7 cents, what 

will | of a yard cost ? f? £ ? 5? A yard ? 

Why ? 

LESSON L X X. 

1 . One half is equal to how many sixths ? 
Ans. Three sixths. Why ? Ans. Since 6 sixths 
make a whole one, ^ of a whole one will bo 
J of 6 sixths, which is 8 sixths. 

2. \ is equal to how many eighths ? Why 4 
eighths ? 

8. Change £ to eighths. Ans. First, f are the 
same as 4, and then 4 may be changed to |; 
therefore f arc the same as |. 

4. Change g to tenths. Why T \ ? 

5. Change £ to thirds. Ans. t = b Why ? 
Ans. J is the same as §, but £ is contained in 
| just as many times as 2 is contained in 4, 
which is 2 times ; therefore | is equal to 2 times 

l '4? which are §. 

6. Change to thirds. To sixths. 








92 PRIMARY ARITHMETIC. 


7. Change ^ to fourths. Ans. ^ — f. 

8. Change ^ to eighths. Ans. First ^ = f, 
and then f = § ; therefore, -fo = |. 

9. Mr. Low worked T \ of a day for me; how 
many fourths of a day did he work? How 
many eighths ? Why ? 

10. 1 paid Mr. Low 9 shillings for T 9 ^ of a 
day’s work; what did I pay him for VV of a 
day ? What for 1 of a day ? What for i of a 
day? Why? 

LESSON LXXI. 

1. Six halves of an apple are the same as 
how many whole apples ? Why 8 ? 

Ans. Since 2 halves of an apple make a whole 
apple, there will be as many whole apples as the 
number of times 2 halves are contained in 6 
halves, which is 3. 

2. How many dollars in 4 halves of a dollar ? 

3. What fraction represents 4 halves ? Ans. |. 

4. In | how many whole ones ? Ans . § = 4 
whole ones. 

5. In J 5 2 - of an apple, how many apples ? 

6. In of a cake, how many cakes ? Why ? 

7. In J e 8 - of a cake, how many cakes ? Why ? 

8. Four whole ones arc how many sixths ? 

9. In 2 whole apples and J of another apple, 
how many fourths of an apple ? Why 9 ? 
Ans. In 2 apples there are f of an apple, and J 
put with f gives f. 

10. How shall two and one fourth be written 
| in figures? H/is. 2J. 









PRIMARY ARITHMETICS 


93 


11. In 3f oranges, how many fifths of an 


orange 


? Am. 3§ oranges == - 1 /- of a11 orange. 


12. At 10 dollars a barrel, 


barrel of flour worth ? § ? 


, what is £ of a 

? H? 2? 2|? 

13. If this pretty bird should sing by your 
window hour every 
day for 8 days, how 
many hours would it 
sing by your window ? 

14. If it should sing 
\ hour every day for 9 
days, how many hours 
would that be ? Am. 
4-£ hours. 

15. If \ of a bushel 
of oats is worth J of a dollar, what is 1 bushel 
worth ? What are 2 bushels worth ? 2i bushels ? 

16. Change 4| to fifths. Am. 2 ^. 

17. Change 3f to sevenths. 

18. Change *£■ to whole ones. Am. 5. 

19. Change -V 8 - to whole ones. 

20. Change to whole ones. Ans. 5f. 

21. Change to whole ones. 

22. How many are r \, ■&, and iV ? Ans. 

j> 

6 * 

23. How many are f, f, f, and f ? Arcs. 

• = 2 . 





_e_ ? 

1 5 • 


24. How many are T 9 X less ? 

25. How many are T 7 T and T 2 T ? 

26. How many are 3 times T 2 X ? 

27. How many are 5 times T 2 T ? 

28. How many are one half of 1£? Ans. 

29. How many arc I of If ? II -f- 5 ? 


13 - - 

* + TT 

Ans. 1 % l 
TT x 4 ? 





PRIMARY ARITHMETIC. 


94 

LESSON L X X11. 

Repeat the following tables: 


UNITED STATES MONEY. 


Mills (m.) make 

1 Cent, marked 

c. 

Cents 

u 

1 Dime, “ 

d. 

Dimes 

a 

1 Dollar, “ 

$ 

Dollars 

a 

1 Eagle, u 

e. 


ENGLISH MONEY. 


Farthings 

(qr-) 

make 1 Penny, 

d. 

Pence 


u 1 Shillings 

s. 

shillings 


“ 1 Pound, 

£. 


TROY WEIGHT. 

24 Grains (gr.) make 1 Pennyweight, dwt. 
20 Pennyweights u 1 Ounce, oz. 

12 Ounces “ 1 Pound, lb. 


APOTHECARIES’ WEIGHT. 


20 Grains (gr.) 

make 

1 Scruple, 

8 Scruples 

u 

1 Dram, 

8 Drams 

u • 

1 Ounce, 

12 Ounces 

66 

1 Pound, 


B 

5 

§ 

lb. 


AVOIRDUPOIS WEIGHT. 

16 Drams (dr.) make 1 Ounce, oz 


16 Ounces “ 

25 Pounds “ 

4 Quarters “ 

20 Hund. Weight “ 


1 Pound, lb. 

1 Quarter, qr. 

1 Hundred Weight, cwt. 
1 Ton, t. 





PRIMARY ARITHMETIC. 

95 j 


CLOTH MEASURE. 

) 

) 

21 Inches (in.) make 

1 Nail, 

11a. 

4 Nails 

u 

1 Quarter, 

qr„ 

4 Quarters 

u 

1 Yard, 

yd. 


LONG MEASURE. 


12 Inches (i 

n.) make 1 Foot, 

ft. 

3 Feet 

u 

1 Yard, 

yd. 

5^ Yards or 

16! Feet, “ 

1 Rod, 

rd. 

40 Rods 

a 

1 Furlong, 

fur. 

8 Furlongs 

a 

1 Mile, 

m. 

691 Statute Miles, nearly, “ 

J 1 Deg. on Circ. 

( of the Earth, 1° 

360 Degrees 

a 

j1 Circum- 
\ ference, 

circ. 


LIQUID MEASURE. 


4 Gills (gi.) 

make 

1 Pint, 

pt. 

2 Pints 

u 

1 Quart, 

qt. 

4 Quarts 

u 

1 Gallon, 

gal. 


DRY MEASURE. . 


2 Pints (pt.) 

make 

1 Quart, 

qt. 

8 Quarts 

u 

1 Peck, 

pk. 

1 4 Pecks 

u 

1 Bushel, 

bush. 

l 

TIME. 



60 Seconds (sec.) 

make 1 Minute 

5, m. 

60 Minutes 


“ 1 Hour, 

h. 

24 Hours 


“ 1 Hay, 

d. 

7 Days 


“ 1 Week, 

wk. 

52 Weeks and I4 Days, or ) 

u 1 Year, 

yr. 

3651 Days, 












96 


PRIMARY ARITHMETIC 




MULTIPLICATION TABLE. 


Once 

1 

is 

1 

44 

2 

44 

2 

a 

3 

a 

3 

a 

4 

u 

4 

u 

5 

u 

5 

a 

6 

u 

6 

u 

7 

44 

7 

44 

8 

u 

8 

a 

9 

44 

9 

u 

10 

u 

10 

u 

11 

(4 

11 

a 

12 

44 

12 

4 times 1 

are 

4 

4 “ 

2 

44 

8 

4 “ 

3 

44 

12 

4 “ 

4 

44 

16 

4 “ 

5 

44 

20 

4 “ 

6 

44 

24 

4 “ 

7 

44 

28 

4 •* 

8 

44 

32 

4 “ 

9 

44 

36 

4 “ 

10 

44 

40 

4 “ 

11 

44 

44 

4 “ 

12 

44 

48 

7 times 1 

are 

7 

7 “ 

2 

44 

14 

7 “ 

3 

44 

21 

7 “ 

4 

4k 

28 

7 “ 

5 

44 

35 

7 “ 

6 

44 

42 

7 “ 

7 

44 

49 

7 “ 

8 

44 

56 

7 “ 

9 

44 

63 

7 “ 

10 

44 

70 

7 “ 

11 

44 

77 

7 “ 

12 

44 

84 

10 times 1 

are 

10 

10 “ 

2 

4k 

20 

10 “ 

3 

44 

30 

10 “ 

4 

44 

40 

10 “ 

5 

k4 

50 

10 « 

6 

44 

60 

10 “ 

7 

44 

70 

10 “ 

8 

U 

80 

10 “ 

9 

44 

90 

10 “ 

10 

44 

100 

10 “ 

11 

44 

110 

10 “ 

12 

44 

120 


2 times 

1 

are 

2 

2 

44 

2 

U 

4 

2 

44 

3 

44 

6 

2 

44 

4 

44 

8 

2 

4 * 

5 


10 

2 

44 

6 

44 

12 

2 

% 4 

7 

44 

14 

2 

44 

8 

44 

16 

2 

44 

9 

44 

18 

2 

44 

10 

44 

20 

2 

44 

11 

44 

22 

2 

44 

12 

44 

24 


5 times 

1 

are 

5 

5 

“ 

2 

“ 

10 

5 

44 

3 

44 

15 

5 

44 

4 

44 

20 

5 

44 

5 

44 

25 

5 

4 4 

6 

44 

30 

5 

44 

7 

44 

35 

5 

44 

8 

44 

40 

5 

44 

9 

44 

45 

5 

44 

10 

44 

50 

5 

44 

11 

44 

55 

5 

44 

12 

44 

60 

8 times 

1 

are 

8 

8 

*4 

2 

44 

16 

8 

(4 

3 

44 

24 

8 

44 

4 

44 

32 

8 

44 

5 

44 

40 

8 

44 

6 

44 

48 

8 

44 

7 

44 

56 

8 

44 

8 

44 

64 

8 

44 

9 

44 

72 

8 

44 

10 

44 

80 

8 

44 

11 

44 

88 

8 

44 

12 

44 

96 

11 times 

1 

are 

11 

11 

44 

2 

44 

22 

11 

44 

3 

44 

33 

11 

44 

4 

44 

44 

11 

44 

5 

44 

55 

11 

44 

6 

44 

66 

11 

44 

7 

44 

77 

11 

44 

8 

44 

88 

11 

44 

9 

44 

99 

11 

44 

10 

44 

110 

11 

44 

11 

44 

121 

11 

44 

12 

44 

132 


3 times 

1 

are 

8 

3 

44 

2 

44 

6 

3 

44 

3 

(4 

9 

3 

44 

4 

44 

12 

3 

44 

5 

44 

15 

3 

4% 

6 

44 

18 

3 

44 

7 

44 

21 

3 

4. 

8 

44 

24 

3 

44 

9 

44 

27 

3 

44 

10 

44 

30 

3 

44 

11 

44 

33 

3 

44 

12 

44 

36 

6 

times 

1 

are 

6 

6 

4» 

2 

44 

12 

6 

44 

3 

44 

18 

6 

44 

4 

4 ( 

24 

6 

44 

5 

44 

30 

6 

44 

6 

44 

36 

6 

k4 

7 

44 

42 

6 

44 

8 

44 

48 

6 

44 

9 

W 

54 

6 

k 4 

10 

44 

60 

6 

44 

11 

44 

66 

6 

44 

12 

44 

72 

9 times 

1 

are 

9 

9 

44 

2' 

44 

18 

9 

44 

3 

44 

27 

9 

44 

4 

44 

36 

9 

44 

5 

44 

45 

9 

44 

6 

44 

54 

9 

44 

7 

44 

63 

9 

44 

8 

44 

72 

9 

4k 

9 

44 

81 

9 

k 4 

10 

44 

90 

9 

44 

11 

44 

99 

9 

4; 

12 

‘•108 

12 times 

1 ; 

are 

12 

12 

4k 

2 

44 

24 

12 

44 

3 


36 

12 

44 

4 

44 

48 

12 

44 

5 

44 

60 

12 

44 

6 

44 

72 

12 

(4 

7 

44 

84 

12 

44 

8 

44 

95 

12 

44 

9 

44 

108 

12 

44 

10 

44 

120 

12 

44 

11 

44 

132 

12 

44 

12 

44 

144 

























PRIMARY ARITHMETIC, 


97 


TABLES FOB REVIEW. 

The following tables may be used to advantage as an 
accompanying exercise to the lessons in the earlier part of 
the book. They should be dwelt upon till the pupil can 
correctly recite them as fast as he can read. 

ADDITION. 

The use of these tables 'may be extended by reading 
each line quite across the page, as, 4 and 2 and 10 and 
5, and so on, and giving the sum of the numbers in the line. 

I. II. III. IY. 


How many are 


4 

and 

2 

10 

and 

5 

5 

and 

5 

10 

and 

10 

9 

and 

4 

9 

and 

6 

4 

and 

4 

11 

and 

4 

5 

and 

6 

8 

and 

1 

4 

and 

8 

6 

and 

11 

3 

and 

2 

G 

and 

6 

7 

and 

5 

5 

and 

12 

4 

and 

7 

10 

and 

8 

2 

and 

2 

3 

and 

13 

9 

and 

5 

9 

and 

9 

10 

and 

9 

11 

and 

5 

10 

and 

1 

5 

and 

4 

11 

and 

2 

14 

and 

6 

7 

and 

6 

10 

and 

2 

4 

and 

3 

3 

and 

14 

8 

and 

7 

8 

and 

3 

8 

and 

8 

13 

and 

5 

5 

and 

2 

3 

and 

2 

9 

and 

8 

11 

and 

9 

9 

and 

8 

9 

and 

3 

12 

and 

3 

5 

and 

14 

G 

and 

3 

7 

and 

9 

3 

and 

3 

12 

and 

6 


Y. 

1 and 2 and 3 

2 and 4 and 1 

3 and 2 and 4 

6 and 3 and 5 
9 and 1 and G 
8 and 7 and 5 

1 and 8 and 8 

2 and 10 and 1 

7 and 8 and G 

4 and 3 and 7 

8 and 5 and 3 

9 and G and 7 


YI. 


How 

many are 

4 

and 

5 

and 

7 

3 

and 

8 

and 

6 

9 

and 

3 

and 

5 

10 

and 

2 

and 

8 

G 

and 

7 

and 

9 

3 

and 

10 

and 

2 

11 

and 

1 

and 

G 

5 

and 

G 

and 

4 

10 

and 

5 

and 

5 

12 

and 

3 

and 

4 

G 

and 

2 

and 

5 

3 

and 

7 

and 

9 


VII. 

11 and 4 and 5 
5 and 4 and 8 

7 and 10 and 7 

12 and 5 and 6 
4 and 5 and 8 
G and 10 and 9 
9 and 11 and 5 

8 and 9 and 9 
3 and G and 2 

13 and 3 and 6 
10 and 10 and 11 
12 and 2 and 8 
















98 


PRIMARY ARITHMETIC, 


TABLES FOR REVIEW. 

SUBTRACTION. 

The following tables can also be made tables in Addi¬ 
tion, by directing the pupil to substitute the word “ and ” 
in each case for the words “ from ” and “ less.” 


I. 

2 from 

6 

7 

II. 

from 

9 

3 

III. 

from 

7 

9 

IY. 

from 

14 

9 

from 

13 

5 

from 

12 

6 

from 

14 

G 

from 

15 

G 

from 

9 

3 

from 

10 

2 

from 

9 

3 

from 

8 

8 

from 

13 

4 

from 

9 

7 

from 

13 

8 

from 

16 

10 from 

14 

3 

from 

12 

9 

from 

17 

5 

from 

13 

2 

from 

8 

4 

from 

8 

4 

from 

G 

3 

from 

G 

G 

from 

11 

9 

from 

11 

7 

from 

14 

10 

from 

1G 

7 

from 

16 

4 

from 

13 

3 

from 

11 

4 

from 

11 

5 

from 

8 

9 

from 

18 

4 

from 

12 

G 

from 

13 

9 

from 

15 

2 

from 

11 

9 

from 

16 

5 

from 

9 

7 

from 

12 

10 

from 

19 

3 

from 

9 

7 

from 

15 

5 

from 

10 

8 

from 

8 

8 

from 

9 i 

G 

from 

10 




A 

DDITION 

AND 

SUBTRACT 

ION, 






1 




II 





HI. 




4 

and 

7 

less 

2 

10 

and 

G 

less 

8 

12 

and 

5 

less 

6 

8 

and 

9 

less 

6 

14 

and 

2 

less 

3 

5 

and 

5 

less 

4 

7 

and 

3 

less 

5 

G 

and 

4 

less 

5 

7 

and 

7 

less 1 

10 

8 

and 

7 

less 

10 

3 

and ] 

11 

less 

7 

14 

and 

7 

less 

1 

4 

and 

2 

less 

3 

4 

and 13 

less 

8 

11 

and 

3 

less 

4 

10 

and 

7 

less 

6 

7 

and 

9 

less 

8 

3 

and 

3 

less 

2 

4 

and 

9 

less 

7 

10 

and 

7 

less 

2 

5 

and 

8 

less 

6 

4 

and 

11 

less 

G 

4 

and 

4 

less 

3 

14 

and 

8 

less 

7 

7 

and 

10 

less 

3 

9 

and 

1 

less 

10 

7 

and 

7 

less 

5 

3 

and 

7 

less 

8 

4 

and 

9 

less 

8 

12 

and 

2 

less 

3 

10 

and 

10 

less 

7 

9 

and 

9 

less 

3 

e 

and 

10 

less 

4 


















PRIMARY ARITHMETIC. 


99 


TABLES FOR REVIEW. 

MULTIPLICATION 

These tables may be converted into lessons in Addition 
by substituting the word “and” for “times,” or into les¬ 
sons in Subtraction by substituting the word “ less ” for 
“ times,” the pupil naming the larger number first. 


2 

I. 

times 

4 

3 

II. 

times 

7 

7 

III. 

times 

10 

3 

IY. 

times 

8 

8 

times 

0 

5 

times 

G 

5 

times 

7 

2 

times 

6 

5 

times 

5 

6 

times 

8 

3 

times 

4 

7 

times 

8 

4 

times 

4 

8 

times 

10 

2 

times 

7 

5 

times 

10 

7 

times 

9 

4 

times 

5 

3 

times 

3 

4 

times 

7 

2 

times 

2 

2 

times 

8 

6 

times 

10 

2 

times 

5 

7 

times 

7 

3 

times 

2 

2 

times 

9 

4 

times 

8 

4 

times 

10 

9 

times 

3 

4 

times 

6 

3 

times 

10 

5 

times 

8 

G 

times 

7 

8 

times 

8 

4 

times 

4 

3 

times 

G 

9 

times 

G 

9 

times 

10 

3 

times 

7 

6 

times 

G 

9 

times 

4 

8 

times 

7 

8 

times 

6 


The Multiplication table of 11 and 12 is here in¬ 
serted, to be learned after the table as far as 10 has 
been learned in a previous part of the book. The pupil 
should learn to recite it as it i3 written, as “ G times 11,” 
and then reverse the order of the figures, as “11 times 


G,” and so on. 



I. 

ii. 

III. 

Once 11 is 11 

Once 12 is 12 

2 times 11 

2 times 11 are 22 

2 times 12 are 24 

3 times 12 

3 times 11 are 33 

3 times 12 are 3G 

12 times 2 

4 times 11 arc 44 

4 times 12 are 48 

8 times 11 

5 times 11 are 55 

5 times 12 are GO 

G times 12 

G times 11 are GG 

G times 12 are 72 

12 times 4 

7 times 11 are 7 7 

7 times 12 are 84 

5 times 11 

8 times 11 are 88 

8 times 12 are 9G 

11 times 7 

9 times 11 are 99 

9 times 1 2 are 108 

10 times 3 

10 times 11 are 110 

10 times 12 are 120 

G times 11 

11 times 11 are 121 

11 times 12 are 132 

7 times 12 

12 times 11 arc 132 

12 times 12 are 144 

> , 

8 times 12 

> 9 h 

L.of 0. 



















100 


PRIMARY ARITHMETIC. 


TABLES FOR REVIEW. 

DIVISION. 

These tables may be converted into Addition and Sub¬ 
traction, by substituting the word “ and ” or “ from ” for 



I 



II. 


III 


IV. 


4 

in 

20 

3 

in 

12 

9 

in 

63 1 

9 

in 

72 

8 

in 

80 

2 

in 

14 

G 

in 

18 

10 

in 

100 

6 

in 

3G 

3 

in 

9 

9 

in 

36 

8 

in 

56 

1 

in 

8 

G 

in 

GO 

10 

in 

70 

10 

in 

50 

6 

in 

54 

2 

in 

18 

3 

in 

24 

7 

in 

28 

2 

in 

8 

8 

in 

G4 

7 

in 

5G 

9 

in 

45 

8 

in 

72 

9 

in 

90 

4 

in 

28 

7 

in 

14 

5 

in 

25 

3 

in 

15 

2 

in 

10 

8 

in 

48 

7 

in 

G3 

9 

in 

81 

3 

in 

30 

7 

in 

42 

3 

in 

18 

5 

in 

30 

5 

in 

45 

9 

in 

27 

5 

in 

40 

G 

in 

42 

7 

in 

70 

9 

in 

54 

4 

in 

3G 

3 

in 

27 

5 

in 

35 

9 

in 

72 


The Division table of 11 and 12 is here inserted, to be 
learned after the table as far as 10 has been completed in 
the previous part of the book. Each question should be 
recited as it stands, and then the order reversed, as “11 
in GG,” then “ G in GG.” 


11 

in 

I. 

11, once. 

12 

in 

ir. 

12, 

once. 

III. 
12 in 

72 

11 

in 

22, 2 

times. 

12 

in 

24, 

2 

times. 

11 

in 

GG 

11 

in 

33, 3 

times. 

12 

in 

36, 

3 

times. 

11 

in 

44 

11 

in 

44, 4 

times. 

12 

in 

48, 

4 

times. 

12 

in 

60 

11 

in 

55, 5 

times. 

12 

in 

GO, 

5 

times. 

12 

in 

24 

11 

in 

GG, G 

times. 

12 

in 

72, 

6 

times. 

2 

in 

24 

11 

in 

77, 7 

times. 

12 

in 

84, 

7 

times. 

11 

in 

77 

11 

in 

88, 8 

times. 

12 

in 

9G, 

8 

times. 

12 

in 

96 

11 

in 

99, 9 

times. 

12 

in 

108, 

9 

times. 

12 

in 

132 

11 

in 

110, 10 

times. 

12 

in 

120, 

10 

times. 

11 

in 

132 

11 

in 

121, 11 

times. 

12 

in 

132, 

11 

times. 

12 

in 

144 

11 

in 

132, 12 

times. 

1 12 

in 

344, 

12 

times. 

11 

in 

22 
























































' - 








































































































































































EATOjV & BRV 0 019 614 082 7 

ERIES OF i IaTHEMATICS, 




Primary, Grammar, High Schools, Academies, 
and Normal Schools, 


ADAPTED TO THE 


L(kte$t kpd rqo^t Sppfoved JVIetl\odd of Iqdtftidtiop. 


100 pages 

176 

G 

324 

»< 

373 

U 

348 

it 

190 

1 4 . 

250 

it 

110 

t < 

125 

it 

235 

ti 

300 

it 


EATON’S Primary Arithmetic. Illustrated . 

EATON’S Intellectual Arithmetic .... 

EATON’S Common-School Arithmetic . 

EATON’S High-School Arithmetic .... 

EATON’S Grammar-School Arithmetic . 

EATON’S Elements of Arithmetic .... 

BRADBURY’S Eaton’s Elementary Algebra 
BRADBURY’S Elementary Geometry. Just published 
BRADBURY’S Elementary Trigonometry, with tables 
BRADBURY’S Geometry, and Trigonometry, in one vol 

Just published. 

BRADBURY’S Trigonometry and Surveying, with tables 

This Series is distinguished by, — 

1. The thorough and scientific manner in which all the principles are devel¬ 

oped and illustrated. 

2. The clearness, precision, and brevity of its rules and definitions. 

3. The logical and satisfactory explanations. 

4. The prominence of Analysis throughout all the books. 

5. The practical character of each book. 

G. The mechanical style in which the books are manufactured. 

They are used in a large portion of the best schools in all parts of 
country with the most satisfactory results. The Arithmetics are so gra-. 
.that a series of three, selected to meet the requirements of particular sch 
systems, will make a complete course of itself. 

4®=* Full Descriptive Catalogue sent o» application. 

“ Eaton’s Arithmetics are found to meet all the xvants of 
schools, and are working well.” — Boston Text-Book Commiti^e. 

THOMPSON, BROWN, & CO., Publishers. 

85 and 89 CornhilX, BOS'! 




- 

























